circles

Let r be the radius of the larger circle. Because the area is $64 \pi$, the radius is 8. 

So, the area of the larger shaded region is half the circumference plus the diameter, which is $\pi r + 2r = 16 + 8 \pi$.

Now, note that the diameter of the smaller circle is the radius of the larger circle, so the radius of the smaller circle is $4$. 

This means that the perimeter of the shaded region is $8 + 4 \pi$, by the formula above. 

So, the total perimeter is $8 + 4 \pi + 16 + 8 \pi = \color{brown}\boxed{24 + 12 \pi}$