This is a question taken from the AMC 2012 12 B exam held in February.

I did not answer it during the exam, but now I try to complete all of it at home. I thought I found a solution, but it is not in the proposed choices, and so I am really lost... And the solution is not available for this question, for some reason.

" Amy, Beth and Jo listen to four different songs and discuss which ones they like. No song is liked by all three. Furthermore, for each of the three pairs of the girls, there is at least one song liked by those two girls but disliked by the third. In how many ways is this possible?

(A) 108 (B) 132 (C) 671 (D) 846 (E) 1105 "

My answer was 168, which is not in the list. Apparently, the answer is supposed to be (B).