jmc

Since $\overline{PA}$ is perpendicular to both $\overline{AB}$ and $\overline{AD}$, the segment $\overline{PA}$ is the altitude from the apex to the base of the pyramid. The area of the base is $[ABCD]=(AB)(BC)=32$, and the height from the apex to the base is 6, so the volume of the pyramid is $\frac{1}{3}(32)(6)=\boxed{64}$ cubic units.