Remember that you're picking 4 balls without replacement.

Thus, A = "you pick 2 green balls" = "you pick 2 green balls and 2 other (non-green balls)". A similar thing happens for B. This means that actually there is an intersection between the two events.

Further, note that any two events have an intersection, it just could be the case that the intersection is the empty set (with probability 0). Hence, if the question was asked where you just picked 2 balls, P(A|B) and P(B|A) would both be 0.

Hope this helps!