P(B|A)=P(A⋂B)/P(A),
7/12=(2/13)/P(A)
P(A)=(2/13)/(7/12)=(2/13)(12/7)=24/91.
To understand this better consider two interlocking circles. One circle, called A, represent the probability of event A; and the other, called B, represents the probability of event B. The region shared by A and B is the probability of the two events occurring together. There are three regions a, b, c, where b is the shared region.
P(A)=a+b, P(B)=b+c. Regions a and c are not part of the interlock.
P(A|B)=b/(b+c) and P(B|A)=b/(a+b). In other words these conditional probabilities are based on the ratio or proportion of the shared region to the probability or region of the "given" event. In this problem A is the given event so we need b/(a+b). We are told b=2/13 and we are told b/(a+b)=7/12.
Therefore 7/12=(2/13)/P(A) from which we can calculate P(A). Note that we don't have enough information to find c, but we can find region a:
b/(a+b)=7/12, 12b=7a+7b, 5b=7a. Since b=2/13, 10/13=7a, a=10/91 (not shared by event B).
All we know about region c (and P(B)=b+c) is that it has to be at least as big as region b.