PUMaC 2014 Geometry B Problem 3

As given in figure (not drawn to proportion), in \triangle A B C, E \in A C, D \in A B, P=B E \cap C D Given that S \triangle B P C=12, while the areas of \triangle B P D, \triangle C P E and quadrilateral A E P D are all the same, which is x. Find the value of x.