How do you explain this in Cartesian Products?

Question

This is how the explanation goes in the textbook:

We have
n(A X B) = n(A) . n(B) = 3 x 2 = 6.

Now every subset of A x B is a relation from A to B and A x B has 2 to the power of 6 subsets.

Therefore the number of different relations from A to B = 2 to the power of 6 = 64

Answer 1

In mathematics, the Cartesian product (or direct product) of two sets X and Y, denoted X × Y, is the set of all possible ordered pairs whose first component is a member of X and whose second component is a member of Y:
The Cartesian product is named after René Descartes whose formulation of analytic geometry gave rise to this concept..☺

Answer 2

Well, what you wrote is pretty clear. What else do you need?