smc

One median divides a triangle into $2$ equal areas, so all three medians will divide a triangle into $6$ equal areas. The median $CE$ is divided into a $2:1$ ratio at centroid $G$, so $GE=\frac{1}{3}\cdot CE=\frac{1}{3}\cdot 12=4$ Similarly, $BG=\frac{2}{3}\cdot 8=\frac{16}{3}$ The area of the right triangle $△BEG$ is $\frac{1}{2}\cdot \frac{16}{3}\cdot 4$ The area of the whole figure is $6\cdot \frac{1}{2}\cdot \frac{16}{3}\cdot 4=64$, and the correct answer is $\boxed{64}$.