The probabilities that A, B, and D can solve a problem independently are $$\dfrac{1}{3},\ \dfrac{1}{3}\ \&\ \dfrac{1}{4}$$ respectively. The probability that only two of them are able to solve the problem is:

There are three cases for exactly two solving it right : 
Case I : A, B solving correct and D going wrong 
                Probability = (1/3)(1/3)(3/4) = 1/12

Case II : A, D solving correct and B going wrong 
                 Probability = (1/3)(2/3)(1/4) = 1/18

Case III : B,D solving correct and A going wrong
                Probability = (2/3)(1/3)(1/4) = 1/18

Therefore, total probability = 1/12 + 1/18 + 1/18 = 1/12 + 1/9 = 7/36