That's a slightly confused syntax, normally either

=SUMPRODUCT(--(MONTH(G2:G174)=2),--(YEAR(G2:G174)=2009))

or

=SUMPRODUCT((MONTH(G2:G174)=2)*(YEAR(G2:G174)=2009))

You could expand the second one to count multiple months like this

=SUMPRODUCT((MONTH(G2:G174)={1,2,3})*(YEAR(G2:G174)=2009))

or just count between the start and end dates

=SUMPRODUCT((G2:G174>=DATE(2009,1,1))*(G2:G174<=DATE(2009,3,31))