The trick is to draw an identical vertical line that is also 4cm away from the vertical dotted line (its the circle's diameter) and a horizontal line that is also 6cm away from the horizontal dotted line (also a diameter).

Notice that the unshaded parts and shaded parts have A,B,C and D in common. The only difference is that the shaded part has 4 more rectangles in the middle , each 4cm by 6cm.

Difference is therefore the arra of 4 rectangles = 4 x 6cm x 4cm = 96cm²