Category of directed multigraphs with loops

Hello, Given two graphs, A and B, I am trying figure out how to construct the product AxB. I have been rereading "Conceptual Mathemtatics" by Lawvere. The category of irreflexive graphs is one of the running examples throughout the book. I have been concentrating on the chapters concerned with the product of objects, but I don't see any details of how to construct AxB. Have I skipped over something? Regards, Bill Halchin