Answer
(a) it increases.
Work Step by Step
General equation connecting charge and potential difference is
$q=CV$
C is constant for the capacitor (as $\kappa$,d and A are kept constant).
Given that $V_{1}=6\,V$ and $V_{2}=12\,V$.
$q_{1}=C\times6\,V$
$q_{2}=C\times12\,V$
Comparing $q_{1}$ and $q_{2}$, we find that $q_{2}\gt q_{1}$. That is, charge on the plate increases.