jmc

Draw a 4 by 8 rectangle with the vertices at $(4,4),(12,4),(12,0)$ and $(4,0)$. The area of that box is $4\times 8=32$ square units. From that we can subtract the area of the sectors of the 2 circles that are binding our shaded region. The area of each sector is $(1/4)4^2\pi =4\pi$; therefore, we need to subtract $2(4\pi )=8\pi$. This gives us $\boxed{32-8\pi }$ square units.