Worksheet_Change Update Multiple Cells with Current Date/Time

Hello, I am attempting to have two separate columns update with the current date when two separate and different columns are updated manually.
So far I was lead to believe that Worksheet_Change Subs in my VBA would be the solution but I cannot get two to work at the same time. I have looked a bit around here in OzGrid and a few other forums but I can't find anything that is clearly describing the solution. I'm not an expert in VBA and I don't fully understand the syntax.
Here is my code, I need to replicate it two more times to trigger from Columns E & F to Column H.

Private Sub Worksheet_Change(ByVal Target As Range)
Dim WorkRng As Range
Dim Rng As Range
Dim xOffsetColumn As Integer
Set WorkRng = Intersect(Application.ActiveSheet.Range("A:A"), Target)
xOffsetColumn = 6
If Not WorkRng Is Nothing Then
    Application.EnableEvents = False
    For Each Rng In WorkRng
        If Not VBA.IsEmpty(Rng.Value) Then
            Rng.Offset(0, xOffsetColumn).Value = Now
            Rng.Offset(0, xOffsetColumn).NumberFormat = "dddd, mmm-dd (hh:mm)"
        Else
            Rng.Offset(0, xOffsetColumn).ClearContents
        End If
    Next
    Application.EnableEvents = True
End If
End Sub

Thanks in advance!
Kelzone52

Sorry for not being super clear. I tried this code but I want the data that is being changed in both column E and F to update Column H, which is only 3 and 2 over with the offset respectively. Otherwise this worked! It triggered for all three columns having a manual data change and input the date as I want, but I need it to put the date for when I update columns E and F into Column H, not just 6 columns over.
Is it possible to get it as three separate triggers so that when A is changed it places the date 6 columns over, but when E is changed it places it 3 columns over, and when F changes it places it 2 columns over?

Thanks much!

Kelzone52

Okay,

When a cell in Column A is updated I want the date to appear in Column G (6 columns over)
When a cell in Column E is updated I want the date to appear in Column H (3 columns over)

When a cell in Column H is updated I want the date to appear in Column H (2 columns over)

So direct and quick reference:
Column A to Column G
Column E to Column H

Column F to Column H

Hopefully this is clear now. Apologies for not making it more clear originally.

Thanks for being patient with me!
Kelzone52

Ah, thank you very much Carim!
What you provided works and I couldn't be happier!

~ Kelzone52