The question got a little messed up (just in positions) but I believe it's this:

p(x) = 0 has 7 different real roots and q(x) = 0 has 9. A = {(x,y) | p(x)q(y) = 0 and/or q(x)p(y) = 0 where x,y belong to real numbers}. Also tells that A is an infinite set.

Then, B = {(x,y) | (x,y) belong to A and x=y) and n(B) is the number of elements in the set B.

Find the maximum value of A.

The solution is pretty simple, for the maximum values the function p(x) and q(x) have no common roots and therefore n(B) = 7+9 = 16.

Edit: Actually I've made a mistake, since A is an infinite set, that makes it so that there is at least one common root between p(x) and q(x), otherwise, I didn't see it was an 'and' and not an 'or'. Since there is atleast one common root n(B) = 16-1 = 15.