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. Applying the Pythagorean Theorem to triangle $ABC$ gives us $AC=\sqrt{13}$. Applying the Pythagorean Theorem to triangle $PAC$ gives us $PA=\sqrt{P{C}^2-A{C}^2}=\sqrt{12}=2\sqrt{3}$.

The area of the base of the pyramid is $[ABCD]=(AB)(BC)=6$, so the volume of the pyramid is $\frac{1}{3}(6)(2\sqrt{3})=\boxed{4\sqrt{3}}$ cubic units.