Two parallel plate capacitors of capacity $$C$$ and $$3C$$ are connected in parallel combination and charged to a potential difference $$18 \text{ V}$$. The battery is then disconnected and the space between the plates of the capacitor of capacity $$C$$ is completely filled with a material of dielectric constant $$9$$. The final potential difference across the combination of capacitors will be ______ V.

Two capacitors $$C$$ and $$3C$$ are connected in parallel and charged to $$18 \text{ V}$$.

Total initial charge:

$$Q = (C + 3C) \times 18 = 72C$$

The battery is disconnected, so charge is conserved.

When a dielectric of constant $$K = 9$$ is inserted in the capacitor of capacity $$C$$, its new capacitance becomes:

$$C' = KC = 9C$$

The new total capacitance of the parallel combination is:

$$C_{total} = 9C + 3C = 12C$$

Since charge is conserved, the new potential difference is:

$$V = \dfrac{Q}{C_{total}} = \dfrac{72C}{12C} = 6 \text{ V}$$

Therefore, the final potential difference is $$\boxed{6}$$ V.