Maybe like:

Option Explicit
  
Sub test()
  MsgBox CountMondays(#6/6/2016#, #6/20/2016#)
End Sub
  
Function CountMondays(ByVal StartingDate As Date, ByVal EndingDate As Date) As Long
Dim d As Date
Dim n As Long
  
  For d = StartingDate To EndingDate
    If Weekday(d, vbMonday) = 1 Then n = n + 1
  Next
  
  CountMondays = n
  
End Function
Mark