Given an ABCD.EFGH cube whose its side length is 8 cm. The point P is within AB so that AP = 3PH. The distance between P to AC is ....

A. $\displaystyle 2\sqrt3$ cm

B. $\displaystyle 3\sqrt3$ cm

C. $\displaystyle 2\sqrt6$ cm

D. $\displaystyle 3\sqrt6$ cm

E. $\displaystyle 4\sqrt6$ cm

So AH is $\displaystyle 8\sqrt2$ cm and PH = $\displaystyle 6\sqrt2$. What do I do now? Is the triangle HPC a right triangle?