Here is a way you can do it :
String initial = "12/06/2014" ;
String newFormat = DateTime.ParseExact(initial, "dd/MM/YYYY").ToString("yyyy-MM-dd");
// newFormat contains now 2014-06-12
EDIT :
ToString() can change the format but it is in string format. how do i
assign the .Tostring() result "yyyy-MM-dd" to date property as it only
accepts the datetime variable in "yyyy-MM-dd" format. if i assign
.Tostring() result in date variable again it is going to change in
"dd/MM/yyyy" format
If you want to assign back the newFormat to a DateTime you must parse it.
DateTime date = DateTime.ParseExact(newFormat , "yyyy-MM-dd");