Quadrilateral $ABCD$ is a parallelogram. Let $E$ be a point on $\overline{AB},$ and let $F$ be the intersection of lines $DE$ and $BC.$ The area of triangle $EBF$ is $4,$ and the area of triangle $EAD$ is $4.$ Find the area of parallelogram $ABCD$.
The area of parallelogram ABCD is 16.