We are given a rectangle $ABCD$ and asked to find the area of triangle $PBQ$. The areas of the smaller triangles are labeled as follows:

• Area of triangle $APB = 36$
• Area of triangle $BCQ = 20$
• Area of triangle $PDQ = 16$

Now let's work step by step:

1. Since $ABCD$ is a rectangle, triangles that share the same height and are between the same parallel sides must have proportional areas based on their base lengths.

2. The entire quadrilateral $PBCQ$ is made up of triangles $PBQ$, $APB$, and $BCQ$. Similarly, quadrilateral $PDQ$ includes triangles $PDQ$ and $PBQ$.

3. Let's assume the height from point $B$ to line $AD$ is the same for all triangles. By comparing areas, we will find the base relationships and solve for the area of $PBQ$.

I'll now perform the calculation to find the area of triangle $PBQ$.