Hello, lemontea!

This is straight-forward.

Exactly where is your difficulty?

The blue circle has center (0,0) and radius 4: .

The red circle has center (0,2) and radius 2: .

The black circle has center (0,-2) and radius 2: .

The shaded region is the area of the blue circle

. . minus the areas of the red and black circles.

Surely you know how to find the area of a circle . . .