Try :
=SUMPRODUCT(((D1:D7=12)+(D1:D7=21)+(D1:D7=23)+(D1: D7=60))*(F1:F7="y"))
HTH
Daniel

I'd like to be able to count the number of "Y" in column H where the values
in column D are equal to 12, 21, 60 or 23.

Any ideas would be appreciated.