Multiple Criteria and Partial Date Matching

If you add a helper column to extract the month/year from column B with formula in D2: =DATE(YEAR(B2),MONTH(B2),1) copied down.

Then you can create a table of products vs. month/year and use COUNTIFS.

So if table is in J1:O7, then in K2:

=COUNTIFS($A:$A,$J2,$D:$D,K$1)

copied across the matrix.

Note: You can also do it without helper columns.. but then you would need SUMPRODUCT() instead of COUNTIFS() and would be much less efficient.