Explanation:

Chiral Hydrocarbon:
A chiral hydrocarbon is a hydrocarbon molecule that lacks a plane of symmetry. It means that the molecule cannot be superimposed onto its mirror image.

Achiral Hydrocarbon:
An achiral hydrocarbon is a hydrocarbon molecule that possesses a plane of symmetry. It means that the molecule can be superimposed onto its mirror image.

Catalytic Hydrogenation:
Catalytic hydrogenation is a chemical reaction in which hydrogen gas (H2) is reacted with a compound in the presence of a catalyst to form a saturated compound. In this process, double bonds are reduced to single bonds, and the compound becomes more saturated.

Analysis of Options:

a) 1-methyl cyclobutene:
- The compound has a double bond and a methyl group attached to the cyclobutene ring.
- The double bond cannot be reduced to a single bond without breaking the ring.
- Hence, it cannot be rendered achiral by catalytic hydrogenation.

b) 3-methyl cyclobutene: (Correct Option)
- The compound has a double bond and a methyl group attached to the cyclobutene ring.
- The double bond can be reduced to a single bond without breaking the ring.
- After catalytic hydrogenation, the compound becomes 3-methyl cyclobutane, which possesses a plane of symmetry.
- Therefore, it is rendered achiral by catalytic hydrogenation.

c) frans-1, 2-dimethyl cyclopropane:
- The compound has two methyl groups attached to the cyclopropane ring.
- The cyclopropane ring cannot be reduced without breaking the ring.
- Hence, it cannot be rendered achiral by catalytic hydrogenation.

d) 2,4-dimethyl-2-hexene:
- The compound has a double bond and two methyl groups attached to the hexene chain.
- The double bond can be reduced to a single bond without breaking the chain.
- After catalytic hydrogenation, the compound becomes 2,4-dimethylhexane, which possesses a plane of symmetry.
- Therefore, it is rendered achiral by catalytic hydrogenation.

Conclusion:
Among the given options, only 3-methyl cyclobutene can be rendered achiral by catalytic hydrogenation.