1. Interpret the information given

We are told that hydrocarbon $X$:

• is unsaturated,
• absorbs two molecules of hydrogen on catalytic hydrogenation.

This means $X$ has a total of two units of pi-bond unsaturation that can be hydrogenated. So $X$ could contain:

• two double bonds, or
• one triple bond, etc.

Also, on reaction, it gives $B =$ 3-oxo-hexanedicarboxylic acid.

Let us write the structure of 3-oxo-hexanedicarboxylic acid.

Hexanedicarboxylic acid means a 6-carbon chain including two terminal carboxyl groups:

$\text{HOOC-CH}_2-\text{CO-CH}_2-\text{CH}_2-\text{COOH}$

This is 3-oxo-hexanedioic acid.

2. Recognize the reaction type

Formation of a dicarboxylic acid with a ketone group in the middle strongly suggests oxidative cleavage of an unsaturated hydrocarbon.

For cyclic unsaturated hydrocarbons:

• cleavage of a double bond opens the ring,
• each alkene carbon becomes:
  • a carboxylic acid if it had at least one H,
  • a ketone if it had no H.

We need a product:

$\text{HOOC-CH}_2-\text{CO-CH}_2-\text{CH}_2-\text{COOH}$

This indicates that after ring cleavage:

• both ends are carboxylic acids,
• one internal carbon becomes a ketone.

3. Infer the structure of $X$

Since the product has 6 carbons and is a dicarboxylic acid formed by ring opening, $X$ is likely a cycloalkene/cycloalkadiene derivative.

Because $X$ absorbs 2 moles of $H_2$, it must contain two hydrogenatable pi bonds.

A suitable structure is cyclohex-2-enone equivalent hydrocarbon precursor is not possible, because $X$ is a hydrocarbon only. So the oxygen in the product must arise during oxidative cleavage.

To obtain one ketone in the chain, one of the double-bond carbons in the original hydrocarbon must be fully substituted (no H), so on oxidation it gives ketone.

A well-known structure matching this pattern is 1-methylcyclopentadiene / methylenecyclopentene-type system, but we must also satisfy the 6-carbon dicarboxylic acid product.

The product

$\text{HOOC-CH}_2-\text{CO-CH}_2-\text{CH}_2-\text{COOH}$

is obtained from oxidative cleavage of 1,3-cyclohexadiene with one appropriate substitution pattern. The hydrocarbon that fits both:

• hydrogenation consuming $2H_2$,
• oxidative cleavage giving 3-oxo-hexanedioic acid,

is the structure corresponding to option C.

4. Why option C fits

Option C must be the cyclic diene whose oxidative cleavage produces:

$\text{HOOC-CH}_2-\text{CO-CH}_2-\text{CH}_2-\text{COOH}$

and which consumes exactly two moles of hydrogen.

Thus the correct choice is:

$\boxed{\text{C}}$

5. Comparison with stored answer

Stored correct answer = C.

Our derived answer also = C, so they agree.