Two capacitors of capacity C and C/3 are connected to a battery of...

The given capacitors having capacitance $C$ and $\dfrac{C}{3}$ are connected in parallel across the battery.

The equivalent capacitance $C_{eq}$ of the circuit is:

$C_{eq} = C + \dfrac{C}{3} = \dfrac{4C}{3}$

The total charge $q$ drawn from the battery to fully charge the capacitors is:

$q = C_{eq}V = \left(\dfrac{4C}{3}\right)V$

The work done $W$ by the battery in supplying this charge is given by the product of the total charge and the potential difference of the battery:

$W = qV$

$W = \left(\dfrac{4CV}{3}\right)V$

$W = \dfrac{4CV^2}{3}$