Verifying if these Cayley tables are from groups b = ac \implies bb = ac \implies e = ac$ but $ac = d$ in the table, so this can't be a group too. Am I rigth?

If all the elements are known to be distinct then you are right in both cases. Else you're first "group" gives you the relation $a=d$ so this could be true and you need to check further, and similarly for the second one.

Also in the first cayley table, notice how the diagonal is just the identity. This tells you that every (nontrivial) element has order 2 and this implies that the "group" is abelian (assuming it is a group), which simplifies matters.