From Gauss's Law, the electric field between the two spherical shells will be the same electric field as that from a point charge $+Q$ at the origin and the electric field outside of both shells will be $0$ .
So, the potential in region $I$ will be
$\begin{align*}\frac{Q}{4 \pi \epsilon_0 r} + V_0\end{align*}$
and the potential in region $II$ will be
$\begin{align*}\frac{Q}{4 \pi \epsilon_0 b} + V_0\end{align*}$
We are told that the potential is $0$ at $r=a$ , so
$\begin{align*}V_0 = \frac{-Q}{4 \pi \epsilon_0 a}\end{align*}$
and answer (D) is correct.

Solution to 2008 Problem 90