Hi,

You can do that with conditional formatting using a formula. Assuming your data is sorted on columns C and D and starts in row 2 with headers in row 1, you would use a formula like
=OR(AND($C1=$C2,$D1=$D2),AND($C3=$C2,$D3=$D2))
applied to the range from A2 to the last cell in column D.

If the data is not sorted, and can't be, the formula would need to change to something like
=COUNTIFS($C:$C,$C2,$D:$D,$D2)>1