A hydrocarbon 'X' with formula C$$_6$$H$$_8$$ uses two moles of H$$_2$$ on catalytic hydrogenation of its one mole. On ozonolysis, 'X' yields two moles of methane dicarbaldehyde. The hydrocarbon 'X' is:

The hydrocarbon X has formula C$$_6$$H$$_8$$.

Degree of unsaturation = $$\frac{2(6) + 2 - 8}{2} = \frac{6}{2} = 3$$

This means 3 degrees of unsaturation (1 ring + 2 double bonds, or other combinations).

Clue 1: Uses 2 moles of H$$_2$$ per mole on catalytic hydrogenation → 2 double bonds (the ring doesn't consume H$$_2$$ under normal catalytic conditions).

Clue 2: Ozonolysis gives 2 moles of methanedicarbaldehyde (OHC-CH$$_2$$-CHO, i.e., malondialdehyde).

Cyclohexa-1,3-diene has 1 ring + 2 double bonds = 3 degrees of unsaturation. On ozonolysis, the two C=C bonds are cleaved, producing two molecules of OHC-CH$$_2$$-CHO (malondialdehyde).

Therefore, X is cyclohexa-1,3-diene.