You'll need a VBA Change Event Code for that...

something like this
Right click on the Sheet's Tab - View code
Paste the following

Private Sub Worksheet_Change(ByVal Target As Range)
Dim myrange As Range, c As Range
Set myrange = Intersect(Target, Range("B:B"))
If Not myrange Is Nothing Then
    For Each c In myrange
        With Cells(c.Row, "A")
            .Value = Format(Now, "YYMMDDhhmmss")
            .NumberFormat = "0"
        End With
    Next c
End If
End Sub