A conducting sphere of radius $R$carrying charge $Q$, lies concentrically  inside an uncharged conducting shell of radius $2R$. When joined by a metal wire

On connecting the conducting sphere having charge $Q$ with a conducting shell having no charge, the entire charge must flow out to the uncharged shell. Option $\left(3\right)$

The capacitance of the outer shell of radius $2R$ is $C\text{'}=4{\mathrm{\pi \epsilon }}_0\left(2\mathrm{R}\right)$
So energy liberated is $U=\frac{Q^2}{2C}=\frac{Q^2}{16\pi {\epsilon }_{0}R}$