Explanation

(d)
Let point $P(x_{1},\ y_{1})$ be any point on the circle, therefore it satisfy the circle
$\left( x_{1} - 3 \right)^{2} + \left( y_{1} + 2 \right)^{2} = 5r^{2}$ …(i)
The length of the tangent drawn from point $P(x_{1},y_{1})$ to the circle
$(x - 3)^{2} + (y + 2)^{2} = r^{2}$ is
$\sqrt{\left( x_{1} - 3 \right)^{2} + \left( y_{1} + 2 \right)^{2} - r^{2}} = \sqrt{5r^{2} - r^{2}}$ [from Eq. (i)]
$\Rightarrow \ \ 16 = 2r\ \ \Rightarrow \ \ r = 8$
$\therefore$ The area between two circles
$= \pi 5r^{2} - \pi r^{2} = 4\pi r^{2} = 4\pi \times 8^{2} = 256\pi$ sq units