Green region minus yellow region

The radius of the green circle is $6+4=10$ . The radius of the yellow circle is $6+4+2=12$ .

The area of the yellow region is equal to the area of the yellow circle minus the area of the green circle and the area of the circle of radius 2. We have

$Y=\pi (12^2)-\pi (10^2) - \pi (2^2)=\pi (144-100-4) = 40 \pi$

The area of the green region is equal to the area of the green circle minus the area of the circle of radius 6 and the area of the circle of radius 4. We have

$G=\pi (10^2) - \pi (6^2) - \pi (4^2)=\pi (100-36-16)=48 \pi$

Therefore,

$G-Y=48 \pi - 40 \pi = \boxed{8 \pi}$