Out of curiosity, if I picked "BUSINESS SUPPORT" and equal your month of May, what answer do you expect?

I get 21 if I also understand your requirements.

=SUMPRODUCT(--(MONTH($C$1)=MONTH(Sheet1!$E$6:$E$14)),--($A3=Sheet1!$A$6:$A$14),Sheet1!$I$6:$I$14)

and this is in column E opn the Skillset Availability tab