Something like this should work:
Public Sub test()
'Loop through cells on "Sheet1"
rowcount1 = 0
Do
rowcount1 = rowcount1 + 1
'Loop through cells on "Sheet2"
rowcount2 = 0
Do
rowcount2 = rowcount2 + 1
item1 = Sheets("Sheet1").Cells(rowcount1, 1)
date1 = Sheets("Sheet1").Cells(rowcount1, 2)
item2 = Sheets("Sheet2").Cells(rowcount2, 1)
date2 = Sheets("Sheet2").Cells(rowcount2, 2)
'Retrieve max date if match found
If item1 = item2 And date2 > date1 Then
Sheets("Sheet1").Cells(rowcount1, 3) = date2
founddate = True
End If
Loop Until Cells(rowcount2, 1) = "" Or founddate = True
founddate = False
Loop Until Sheets("Sheet1").Cells(rowcount1, 1) = ""
End Sub
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