4. Given point $P(x, y)$ satisfies $(x-4 \cos \theta)^{2}+$ $(y-4 \sin \theta)^{2}=4(\theta \in \mathbf{R})$. Then the area of the region where point $P(x, y)$ is located is ( ).
(A) $36 \pi$
(B) $32 \pi$
(C) $20 \pi$
(D) $16 \pi$
4.B.

The points that satisfy the condition lie within the annulus centered at $(0,0)$ with radii 2 and 6, and its area is $36 \pi-4 \pi=32 \pi$.