A solid metal sphere of radius R has a charge $+2Q$. A hollow spherical shell of radius 3R placed concentric with the first sphere has net charge $-Q$. Calculate the potential difference between the spheres.

After the charge distribution, charges at the surfaces are as shown in figure. 

potential at inner sphere

${\mathrm{V}}_1=\frac{2\mathrm{Q}}{4{\mathrm{\pi \epsilon }}_0\mathrm{R}}-\frac{2\mathrm{Q}}{4{\mathrm{\pi \epsilon }}_0\left(3\mathrm{R}\right)}+\frac{\mathrm{Q}}{4{\mathrm{\pi \epsilon }}_0\left(3\mathrm{R}\right)}=\frac{5\mathrm{Q}}{12{\mathrm{\pi \epsilon }}_0\mathrm{R}}$

At outer sphere

$\begin{array}{l}{\mathrm{V}}_2=\frac{2\mathrm{Q}}{4{\mathrm{\pi \epsilon }}_0\left(3\mathrm{R}\right)}-\frac{2\mathrm{Q}}{4{\mathrm{\pi \epsilon }}_0\left(3\mathrm{R}\right)}+\frac{\mathrm{Q}}{4{\mathrm{\pi \epsilon }}_0\left(3\mathrm{R}\right)}=\frac{\mathrm{Q}}{12{\mathrm{\pi \epsilon }}_0\mathrm{R}}\\ \Rightarrow {\mathrm{V}}_1-{\mathrm{V}}_2=\frac{5\mathrm{Q}}{12{\mathrm{\pi \epsilon }}_0\mathrm{R}}-\frac{\mathrm{Q}}{12{\mathrm{\pi \epsilon }}_0\mathrm{R}}=\frac{\mathrm{Q}}{3{\mathrm{\pi \epsilon }}_0\mathrm{R}}\end{array}$