Try this code, note that I used range names, "date1" for the date to be cleared (or not), "select1" for the cell containing the selection form the validation list, and "list1" for the validation list.
Private Sub Worksheet_Change(ByVal Target As Range)
Dim List_Item As Integer
Static old_value As Variant
If ActiveSheet.Range("select1").Value <> old_value Then
List_Item = WorksheetFunction.Match(Range("select1").Value, Range("list1"), 0)
Select Case List_Item
'Note.. the following criteria is a simple example, change as necessary.
'This says if the selected item is either the first three items in the list,
'clear the date, or if it is the 6'th item in the list.
Case Is < 4
Range("date1").ClearContents
Case Is = 6
Range("date1").ClearContents
End Select
old_value = ActiveSheet.Range("select1")
End If
End Sub