I need to have this section of code modified to include a wide range of
W3:w6000, Z3:Z6000, AH3:AH6000. How would one accomplish that?

See code that follows:
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Private Sub Worksheet_Change(ByVal Target As Range)
'Plugging the starting value in column Z and increasing it incrementally
If Target.Address < "$AH$3" Then Exit Sub
Application.EnableEvents = False
Range("W3").Value = Range("W3").Value + 1
Range("Z3").Value = Range("Z3").Value + Target.Value
Application.EnableEvents = True
End Sub
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THanks,