I have this Enum code:
enum Duration { Day, Week, Month };
Can I add a extension methods for this Enum?
You can create an extension for anything, even object(although that's not considered best-practice). Understand an extension method just as a public static method. You can use whatever parameter-type you like on methods.
public static class DurationExtensions
{
public static int CalculateDistanceBetween(this Duration first, Duration last)
{
//Do something here
}
}