2020 AMC 10B Problem 8

Points P and Q lie in a plane with PQ=8. How many locations for point R in this plane are there such that the triangle with vertices P, Q, and R is a right triangle with area 12 square units?

\textbf{(A)}\ 2 \qquad\textbf{(B)}\ 4 \qquad\textbf{(C)}\ 6 \qquad\textbf{(D)}\ 8 \qquad\textbf{(E)}\ 12

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.