T. Valko wrote...
That's the same as:

=COUNTIF(A1:A10,C1)+COUNTIF(B1:B10,D1)

The OP wanted the count where both criteria are on the same row.
....

You're right. It'd need to be something like

=COUNT(1/(MMULT(--(A1:B10=C1:D1),{1;1})=2))

but nothing gained with just two sets of comparisons.