jmc

Since $\angle BAD=60^{\circ }$, isosceles $△BAD$ is also equilateral. As a consequence, $△AEB$, $△AED$, $△BED$, $△BFD$, $△BFC$, and $△CFD$ are congruent. These six triangles have equal areas and their union forms rhombus $ABCD$, so each has area $24/6=4$. Rhombus $BFDE$ is the union of $△BED$ and $△BFD$, so its area is $\boxed{8}.$