Answer
for $A\subseteq B$
Work Step by Step
"The intersection of A with B has as many elements as A"
This is possible only if A is contained in B, or equal to B.
if $A\subseteq B$
Proof: If there were an element in A, which is not in the intersection,
then the cardinality of A would be greater than the cardinality of the intersection.
Since this is not so, the x doesn't exist.
The intersection is the set A.
Since the intersection is a subset of B, so is A.