Answer
That region is represented in the following image:
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Work Step by Step
1. Since the angle $\theta$ is greater or equal than $\pi$ and less or equal than $\frac{3\pi} 2$, the region to be sketched is completely in the third quadrant (for positive values of $r$).
2. As $r$ goes from $0$ to $2$, it contains all the circles with: $0 \leq radius \lt 2$. Thus, we can draw a circle with radius equal to 2 (that isn't in the region sketched), and sketch all the region inside that circle, in the third quadrant.
