|Right click the worksheet tab for the sheet you want this to happen in.|
Paste the following code into the pane that opens.
Whenever you change a cell in Column 1 (A), the current time and date will be placed in Column B. Format the cells as as desired.
It should be obvious what changes to make if Columns A & B are not the columns you are working with.
Private Sub Worksheet_Change(ByVal Target As Range)
If Target.Column = 1 Then _
Range("B" & Target.Row) = Now
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