Quote by PennState666
What would the elements of Z2 x Z3 look like again?

Well, if A and B are any sets (whether or not they have a group structure), then what is the definition of A x B? This is called the Cartesian product of A and B. The elements are simply ordered pairs of the form [itex](a,b)[/itex], where [itex]a \in A[/itex] and [itex]b \in B[/itex].
And if A and B are groups, then there's a natural way to define a group operation on A x B.
Surely this is discussed in your textbook or lecture? There's no way you can proceed with this problem without first understanding what the group is.