First, your suggested formula of A1*B is not valid.
Second, reread the OP's question. If I'm not mistaken he has something like this:
1 Prod_A 3
2 Prod_B 4
3 Prod_A 6
4 Prod_A 3
5 Prod_B 2
He is looking for the total number of each product ordered.
=SUMIF(A1:A5, "Prod_A", B1:B5) will return 12
Posting Tip: Before posting Data or VBA Code, read this How-To.