Problem:

The following formula was written to count the number of dates in column A that matched the month criteria in cell B2.
=COUNTIF(MONTH(A2:A6),B2)
However, on entry, an error occurred and the formula could not be used.

Solution 1:

Use the SUMPRODUCT and MONTH functions as shown in the following formula:
=SUMPRODUCT(--(MONTH(A2:A6)=B2))

Solution 2:

Use the SUM, IF, and MONTH functions as shown in the following Array formula:
{=SUM(IF(MONTH(A2:A6)=B2,1))}