This might not be the most straightforward method, but you can find the area of the trapezoid ABCD. Then note that triangle ABE is similar to triangle FGE.
Hint: Length FG is 3 units in length, and because triangle EAB is similar to triangle EFG, and length AB is 6 units, the scaling factor for the lengths is 2, and thus the scaling factor for the areas is 4.