I am trying to figure out how to move the items in a pre-populated listbox up and down via mouse drags.
I have looked at the Control.DoDragDrop method from microsof
Repair code :
private void listbox1_Drop(object sender, DragEventArgs e)
{
    if (sender is ListBoxItem)
    {
        Emp droppedData = e.Data.GetData(typeof(Emp)) as Emp;
        Emp target = ((ListBoxItem)(sender)).DataContext as Emp;
        int removedIdx = listbox1.Items.IndexOf(droppedData);
        int targetIdx = listbox1.Items.IndexOf(target);
        if (removedIdx < targetIdx)
        {
            _empList.Insert(targetIdx + 1, droppedData);
            _empList.RemoveAt(removedIdx);
        }
        else
        {
            int remIdx = removedIdx + 1;
            if (_empList.Count + 1 > remIdx)
            {
                _empList.Insert(targetIdx, droppedData);
                _empList.RemoveAt(remIdx);
            }
        }
    }
}
                                                                        Improving upon Wiesław Šoltés's modification of dnr3's answer, I abstracted this out into an easily-reusable class, so that you can set up multiple of these lists with only a few lines of code. I also added a feature whereby each item alternates between 2 background colours, for easier viewing (though this feature can easily be removed, if you don't want it).
F.Y.I: Sorry if you're a lover of 'var', but I am absolutely not and those got removed by my IDE, and I don't intend to put them back. Of course this changes nothing about the actual program behaviour and should improve compile-time anyway, so.. winning! :p
Here is the class:
/// <typeparam name="IT">The item type to be stored in this list</typeparam>
internal class ReorderableList<IT> where IT : class
{
    private readonly SolidColorBrush m_alternator1, m_alternator2; // Background colours for the list items to alternate between
    private readonly ListBox m_ListBox; // The target ListBox we're modifying
    private readonly string m_displayMemberPath; // The name of the member in to display 
    private readonly IList<IT> m_items = new ObservableCollection<IT>();
    private Point m_cursorStartPos;
    /// <summary>
    /// Initializes the list (this must be done after components are initialized and loaded!).
    /// </summary>
    /// <param name="resourceProvider">Pass 'this' for this parameter</param>
    /// <param name="listBox">The target ListBox control to modify</param>
    /// <param name="displayMemberPath">The name of the member in the generic type contained in this list, to be displayed</param>
    public ReorderableList(ListBox listBox, string displayMemberPath, SolidColorBrush alternator1, SolidColorBrush alternator2)
    {
        m_ListBox = listBox;
        m_displayMemberPath = displayMemberPath;
        m_alternator1 = alternator1;
        m_alternator2 = alternator2;
        Initialize();
    }
    private void Initialize()
    {
        // Set the list box's items source and tell it what member in the IT class to use for the display name
        // Add an event handler for preview mouse move
        m_ListBox.DisplayMemberPath = m_displayMemberPath;
        m_ListBox.ItemsSource = m_items;
        m_ListBox.PreviewMouseMove += OnListPreviewMouseMove;
        // Create the item container style to be used by the listbox
        // Add mouse event handlers to the style
        Style style = new Style(typeof(ListBoxItem));
        style.Setters.Add(new Setter(UIElement.AllowDropProperty, true));
        style.Setters.Add(new EventSetter(UIElement.PreviewMouseLeftButtonDownEvent, new MouseButtonEventHandler(OnListPreviewMouseLeftButtonDown)));
        style.Setters.Add(new EventSetter(UIElement.DropEvent, new DragEventHandler(OnListDrop)));
        // Add triggers to alternate the background colour of each element based on its alternation index
        // (Remove this, as well as the two SolidColorBrush resources if you don't want this feature)
        Trigger trigger1 = new Trigger()
        {
            Property = ItemsControl.AlternationIndexProperty,
            Value = 0
        };
        Setter setter1 = new Setter()
        {
            Property = Control.BackgroundProperty,
            Value = m_alternator1
        };
        trigger1.Setters.Add(setter1);
        style.Triggers.Add(trigger1);
        Trigger trigger2 = new Trigger()
        {
            Property = ItemsControl.AlternationIndexProperty,
            Value = 1
        };
        Setter setter2 = new Setter()
        {
            Property = Control.BackgroundProperty,
            Value = m_alternator2
        };
        trigger2.Setters.Add(setter2);
        style.Triggers.Add(trigger2);
        // Set the item container style
        m_ListBox.ItemContainerStyle = style;
    }
    /// <summary>
    /// Adds an item to the list. If [ignoreDuplicates] is false and the item is already in the list,
    /// the item won't be added.
    /// </summary>
    /// <param name="item">The item to add</param>
    /// <param name="ignoreDuplicates">Whether or not to add the item regardless of whether it's already in the list</param>
    /// <returns>Whether or not the item was added</returns>
    public bool Add(IT item, bool ignoreDuplicates = true)
    {
        if (!ignoreDuplicates && Contains(item)) return false;
        m_items.Add(item);
        return true;
    }
    /// <summary>
    /// Removes an item from the list.
    /// </summary>
    /// <param name="item">The item to remove</param>
    /// <returns>Whether or not the item was removed from the list. This will be false if the item was not in the list to begin with.</returns>
    public bool Remove(IT item)
    {
        if (Contains(item)) return false;
        m_items.Remove(item);
        return true;
    }
    /// <summary>
    /// Returns whether or not the list contains the given item.
    /// </summary>
    /// <param name="item">The item to check for</param>
    /// <returns>Whether or not the list contains the given item.</returns>
    public bool Contains(IT item)
    {
        return m_items.Contains(item);
    }
    private void OnListPreviewMouseLeftButtonDown(object sender, MouseButtonEventArgs e)
    {
        m_cursorStartPos = e.GetPosition(null);
    }
    private void OnListPreviewMouseMove(object sender, MouseEventArgs e)
    {
        Point currentCursorPos = e.GetPosition(null);
        Vector cursorVector = m_cursorStartPos - currentCursorPos;
        if (e.LeftButton == MouseButtonState.Pressed
            &&(Math.Abs(cursorVector.X) > SystemParameters.MinimumHorizontalDragDistance
            || Math.Abs(cursorVector.Y) > SystemParameters.MinimumVerticalDragDistance))
        {
            ListBoxItem targetItem = FindVisualParent<ListBoxItem>(((DependencyObject)e.OriginalSource));
            if (targetItem != null)
            {
                DragDrop.DoDragDrop(targetItem, targetItem.DataContext, DragDropEffects.Move);
            }
        }
    }
    private void OnListDrop(object sender, DragEventArgs e)
    {
        if (sender is ListBoxItem item)
        {
            IT source = e.Data.GetData(typeof(IT)) as IT;
            IT target = item.DataContext as IT;
            int sourceIndex = m_ListBox.Items.IndexOf(source);
            int targetIndex = m_ListBox.Items.IndexOf(target);
            Move(source, sourceIndex, targetIndex);
        }
    }
    private void Move(IT source, int sourceIndex, int targetIndex)
    {
        if (sourceIndex < targetIndex)
        {
            m_items.Insert(targetIndex + 1, source);
            m_items.RemoveAt(sourceIndex);
        }
        else
        {
            int removeIndex = sourceIndex + 1;
            if (m_items.Count + 1 > removeIndex)
            {
                m_items.Insert(targetIndex, source);
                m_items.RemoveAt(removeIndex);
            }
        }
    }
    private T FindVisualParent<T>(DependencyObject child) where T : DependencyObject
    {
        DependencyObject parentObject = VisualTreeHelper.GetParent(child);
        if (parentObject == null) return null;
        if (parentObject is T parent) return parent;
        return FindVisualParent<T>(parentObject);
    }
}
And here is an example IT (item type) class (same as in the original answer):
public class ExampleItem
{
    public string Name { get; set; }
    public ExampleItem(string name)
    {
        Name = name;
    }
}
And finally, the usage:
public partial class MainWindow : Window
{
    private readonly ReorderableList<ExampleItem> ExampleList;
    public MainWindow()
    {
        InitializeComponent();
        ExampleList = new ReorderableList<ExampleItem>(myXamlListBoxControl, "Name",
            FindResource("AlternatingBG1") as SolidColorBrush,
            FindResource("AlternatingBG2") as SolidColorBrush);
        ExampleList.Add(new ExampleItem("Test Item 1"));
        ExampleList.Add(new ExampleItem("Test Item 2"));
        ExampleList.Add(new ExampleItem("Test Item 3"));
        ExampleList.Add(new ExampleItem("Test Item 4"));
        ExampleList.Add(new ExampleItem("Test Item 5"));
        ExampleList.Add(new ExampleItem("Test Item 6"));
    }
}
                                                                        This has helped me greatly thank you. Especially the generics version.
I made the following amendments:
Because I don't set the DataContext of the ListBox (just the ItemsSource), I use
var items = this.ItemsSource as IList<T>;
in the Move method.
And at the end of "Move" I added:
this.SelectedItem = source;
as I want the user to have the moved item as the current selection.
I took dnr3's answer and altered it for implementation in XAML. Same result, just prefer doing what I can in XAML rather than in the code-behind.
In place of the code-behind:
Style itemContainerStyle = new Style(typeof(ListBoxItem));
itemContainerStyle.Setters.Add(new Setter(AllowDropProperty, true));
itemContainerStyle.Setters.Add(new EventSetter(PreviewMouseLeftButtonDownEvent, new MouseButtonEventHandler(s_PreviewMouseLeftButtonDown)));
itemContainerStyle.Setters.Add(new EventSetter(DropEvent, new DragEventHandler(listbox1_Drop)));
listbox1.ItemContainerStyle = itemContainerStyle;
Put this in the XAML:
<Window.Resources>
    <Style x:Key="ListBoxDragDrop" TargetType="{x:Type ListBoxItem}">
        <Setter Property="AllowDrop" Value="true"/>
        <EventSetter Event="PreviewMouseMove" Handler="s_PreviewMouseMoveEvent"/>
        <EventSetter Event="Drop" Handler="listbox1_Drop"/>
    </Style>
</Window.Resources>
<Grid>
    <ListBox x:Name="listbox1" ItemContainerStyle="{StaticResource ListBoxDragDrop}" HorizontalAlignment="Left" Height="299" Margin="10,10,0,0" VerticalAlignment="Top" Width="224"/>
</Grid>
This is mouse-handler placed in the code-behind of the XAML.
void s_PreviewMouseMoveEvent(object sender, MouseEventArgs e)
{
    if (sender is ListBoxItem && e.LeftButton == MouseButtonState.Pressed)
    {
        ListBoxItem draggedItem = sender as ListBoxItem;
        DragDrop.DoDragDrop(draggedItem, draggedItem.DataContext, DragDropEffects.Move);
        draggedItem.IsSelected = true;
    }
}
                                                                        Using dnr3's answers I have created version with fixed selection issues.
Window1.xaml
<Window x:Class="ListBoxReorderDemo.Window1"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        Title="ListBoxReorderDemo" Height="300" Width="300"
        WindowStartupLocation="CenterScreen">
    <Grid>
        <ListBox x:Name="listBox"/>
    </Grid>
</Window>
Window1.xaml.cs
using System;
using System.Collections.Generic;
using System.Collections.ObjectModel;
using System.Text;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
namespace ListBoxReorderDemo
{
    public class Item
    {
        public string Name { get; set; }
        public Item(string name)
        {
            this.Name = name;
        }
    }
    public partial class Window1 : Window
    {
        private Point _dragStartPoint;
        private T FindVisualParent<T>(DependencyObject child)
            where T : DependencyObject
        {
            var parentObject = VisualTreeHelper.GetParent(child);
            if (parentObject == null)
                return null;
            T parent = parentObject as T;
            if (parent != null)
                return parent;
            return FindVisualParent<T>(parentObject);
        }
        private IList<Item> _items = new ObservableCollection<Item>();
        public Window1()
        {
            InitializeComponent();
            _items.Add(new Item("1"));
            _items.Add(new Item("2"));
            _items.Add(new Item("3"));
            _items.Add(new Item("4"));
            _items.Add(new Item("5"));
            _items.Add(new Item("6"));
            listBox.DisplayMemberPath = "Name";
            listBox.ItemsSource = _items;
            listBox.PreviewMouseMove += ListBox_PreviewMouseMove;
            var style = new Style(typeof(ListBoxItem));
            style.Setters.Add(new Setter(ListBoxItem.AllowDropProperty, true));
            style.Setters.Add(
                new EventSetter(
                    ListBoxItem.PreviewMouseLeftButtonDownEvent,
                    new MouseButtonEventHandler(ListBoxItem_PreviewMouseLeftButtonDown)));
            style.Setters.Add(
                    new EventSetter(
                        ListBoxItem.DropEvent, 
                        new DragEventHandler(ListBoxItem_Drop)));
            listBox.ItemContainerStyle = style;
        }
        private void ListBox_PreviewMouseMove(object sender, MouseEventArgs e)
        {
            Point point = e.GetPosition(null);
            Vector diff = _dragStartPoint - point;
            if (e.LeftButton == MouseButtonState.Pressed &&
                (Math.Abs(diff.X) > SystemParameters.MinimumHorizontalDragDistance ||
                    Math.Abs(diff.Y) > SystemParameters.MinimumVerticalDragDistance))
            {
                var lb = sender as ListBox;
                var lbi = FindVisualParent<ListBoxItem>(((DependencyObject)e.OriginalSource));
                if (lbi != null)
                {
                    DragDrop.DoDragDrop(lbi, lbi.DataContext, DragDropEffects.Move);
                }
            }
        }
        private void ListBoxItem_PreviewMouseLeftButtonDown(object sender, MouseButtonEventArgs e)
        {
            _dragStartPoint = e.GetPosition(null);
        }
        private void ListBoxItem_Drop(object sender, DragEventArgs e)
        {
            if (sender is ListBoxItem)
            {
                var source = e.Data.GetData(typeof(Item)) as Item;
                var target = ((ListBoxItem)(sender)).DataContext as Item;
                int sourceIndex = listBox.Items.IndexOf(source);
                int targetIndex = listBox.Items.IndexOf(target);
                Move(source, sourceIndex, targetIndex);
            }
        }
        private void Move(Item source, int sourceIndex, int targetIndex)
        {
            if (sourceIndex < targetIndex)
            {
                _items.Insert(targetIndex + 1, source);
                _items.RemoveAt(sourceIndex);
            }
            else
            {
                int removeIndex = sourceIndex + 1;
                if (_items.Count + 1 > removeIndex)
                {
                    _items.Insert(targetIndex, source);
                    _items.RemoveAt(removeIndex);
                }
            }
        }
    }
}
Version with support for generics and data binding.
Window1.xaml
<Window x:Class="ListBoxReorderDemo.Window1"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:local="clr-namespace:ListBoxReorderDemo"
        Title="ListBoxReorderDemo" Height="300" Width="300"
        WindowStartupLocation="CenterScreen">
    <Grid>
        <local:ItemDragAndDropListBox x:Name="listBox" ItemsSource="{Binding}">
            <ListBox.ItemTemplate>
                <DataTemplate>
                    <TextBlock Text="{Binding Name}"/>
                </DataTemplate>
            </ListBox.ItemTemplate>
        </local:ItemDragAndDropListBox>
    </Grid>
</Window>
Window1.xaml.cs
using System;
using System.Collections.Generic;
using System.Collections.ObjectModel;
using System.Text;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
namespace ListBoxReorderDemo
{
    public class DragAndDropListBox<T> : ListBox 
        where T : class
    {
        private Point _dragStartPoint;
        private P FindVisualParent<P>(DependencyObject child) 
            where P : DependencyObject
        {
            var parentObject = VisualTreeHelper.GetParent(child);
            if (parentObject == null)
                return null;
            P parent = parentObject as P;
            if (parent != null)
                return parent;
            return FindVisualParent<P>(parentObject);
        }
        public DragAndDropListBox()
        {
            this.PreviewMouseMove += ListBox_PreviewMouseMove;
            var style = new Style(typeof(ListBoxItem));
            style.Setters.Add(new Setter(ListBoxItem.AllowDropProperty, true));
            style.Setters.Add(
                new EventSetter(
                    ListBoxItem.PreviewMouseLeftButtonDownEvent,
                    new MouseButtonEventHandler(ListBoxItem_PreviewMouseLeftButtonDown)));
            style.Setters.Add(
                    new EventSetter(
                        ListBoxItem.DropEvent, 
                        new DragEventHandler(ListBoxItem_Drop)));
            this.ItemContainerStyle = style;
        }
        private void ListBox_PreviewMouseMove(object sender, MouseEventArgs e)
        {
            Point point = e.GetPosition(null);
            Vector diff = _dragStartPoint - point;
            if (e.LeftButton == MouseButtonState.Pressed &&
                (Math.Abs(diff.X) > SystemParameters.MinimumHorizontalDragDistance ||
                    Math.Abs(diff.Y) > SystemParameters.MinimumVerticalDragDistance))
            {
                var lb = sender as ListBox;
                var lbi = FindVisualParent<ListBoxItem>(((DependencyObject)e.OriginalSource));
                if (lbi != null)
                {
                    DragDrop.DoDragDrop(lbi, lbi.DataContext, DragDropEffects.Move);
                }
            }
        }
        private void ListBoxItem_PreviewMouseLeftButtonDown(object sender, MouseButtonEventArgs e)
        {
            _dragStartPoint = e.GetPosition(null);
        }
        private void ListBoxItem_Drop(object sender, DragEventArgs e)
        {
            if (sender is ListBoxItem)
            {
                var source = e.Data.GetData(typeof(T)) as T;
                var target = ((ListBoxItem)(sender)).DataContext as T;
                int sourceIndex = this.Items.IndexOf(source);
                int targetIndex = this.Items.IndexOf(target);
                Move(source, sourceIndex, targetIndex);
            }
        }
        private void Move(T source, int sourceIndex, int targetIndex)
        {
            if (sourceIndex < targetIndex)
            {
                var items = this.DataContext as IList<T>;
                if (items != null)
                {
                    items.Insert(targetIndex + 1, source);
                    items.RemoveAt(sourceIndex);
                }
            }
            else
            {
                var items = this.DataContext as IList<T>;
                if (items != null)
                {
                    int removeIndex = sourceIndex + 1;
                    if (items.Count + 1 > removeIndex)
                    {
                        items.Insert(targetIndex, source);
                        items.RemoveAt(removeIndex);
                    }
                }
            }
        }
    }
    public class Item
    {
        public string Name { get; set; }
        public Item(string name)
        {
            this.Name = name;
        }
    }
    public class ItemDragAndDropListBox : DragAndDropListBox<Item> { }
    public partial class Window1 : Window
    {
        private IList<Item> _items = new ObservableCollection<Item>();
        public Window1()
        {
            InitializeComponent();
            _items.Add(new Item("1"));
            _items.Add(new Item("2"));
            _items.Add(new Item("3"));
            _items.Add(new Item("4"));
            _items.Add(new Item("5"));
            _items.Add(new Item("6"));
            listBox.DataContext = _items;
        }
    }
}
                                                                        i've tried create one using observablecollection, have a look
    ObservableCollection<Emp> _empList = new ObservableCollection<Emp>();
    public Window1()
    {
        InitializeComponent();
        _empList .Add(new Emp("1", 22));
        _empList .Add(new Emp("2", 18));
        _empList .Add(new Emp("3", 29));
        _empList .Add(new Emp("4", 9));
        _empList .Add(new Emp("5", 29));
        _empList .Add(new Emp("6", 9));
        listbox1.DisplayMemberPath = "Name";
        listbox1.ItemsSource = _empList;
        Style itemContainerStyle = new Style(typeof(ListBoxItem));
        itemContainerStyle.Setters.Add(new Setter(ListBoxItem.AllowDropProperty, true));
        itemContainerStyle.Setters.Add(new EventSetter(ListBoxItem.PreviewMouseLeftButtonDownEvent, new MouseButtonEventHandler(s_PreviewMouseLeftButtonDown)));
        itemContainerStyle.Setters.Add(new EventSetter(ListBoxItem.DropEvent, new DragEventHandler(listbox1_Drop)));
        listbox1.ItemContainerStyle = itemContainerStyle;
    }
Drag and drop process
    void s_PreviewMouseLeftButtonDown(object sender, MouseButtonEventArgs e)
    {
        if (sender is ListBoxItem)
        {
            ListBoxItem draggedItem = sender as ListBoxItem;
            DragDrop.DoDragDrop(draggedItem, draggedItem.DataContext, DragDropEffects.Move);
            draggedItem.IsSelected = true;
        }
    }
    void listbox1_Drop(object sender, DragEventArgs e)
    {
        Emp droppedData = e.Data.GetData(typeof(Emp)) as Emp;
        Emp target = ((ListBoxItem)(sender)).DataContext as Emp;
        int removedIdx = listbox1.Items.IndexOf(droppedData);
        int targetIdx = listbox1.Items.IndexOf(target);
        if (removedIdx < targetIdx)
        {
            _empList.Insert(targetIdx + 1, droppedData);
            _empList.RemoveAt(removedIdx);
        }
        else
        {
            int remIdx = removedIdx+1;
            if (_empList.Count + 1 > remIdx)
            {
                _empList.Insert(targetIdx, droppedData);
                _empList.RemoveAt(remIdx);
            }
        }
    }
Note:
PreviewMouseLeftButtonDown event, the dragged item looks like not selected