A thin metal plate P is inserted between the plates of a...

When the thin metal plate $P$ is inserted such that its edges make contact with both plates of the capacitor, it effectively short-circuits the two plates.

Because the plates are connected by a conducting material, the potential difference $V$ between them becomes zero for any finite charge.

The capacitance of a capacitor is defined as $C = \dfrac{Q}{V}$.

Substituting $V = 0$, the new capacitance becomes $C' = \dfrac{Q}{0} \rightarrow \infty$.

Therefore, the new capacitance is infinite.