Explanation:

The carbon-carbon bond length in a molecule is determined by the type of bond present between the carbon atoms. There are three types of carbon-carbon bonds: single bonds, double bonds, and triple bonds. The bond length decreases as the bond order increases.

Benzene:
Benzene is a cyclic compound consisting of six carbon atoms bonded together in a ring with alternating single and double bonds. The bond order between each pair of carbon atoms is 1.5, which is an average between a single bond and a double bond. The carbon-carbon bond length in benzene is longer than that in a typical single bond but shorter than that in a typical double bond.

Ethene:
Ethene, also known as ethylene, is an unsaturated hydrocarbon with a double bond between two carbon atoms. The bond order between the carbon atoms in ethene is 2. The carbon-carbon bond length in ethene is shorter than that in benzene because it is a double bond.

Ethyne:
Ethyne, also known as acetylene, is an unsaturated hydrocarbon with a triple bond between two carbon atoms. The bond order between the carbon atoms in ethyne is 3. The carbon-carbon bond length in ethyne is shorter than that in ethene because it is a triple bond.

Ethane:
Ethane is a saturated hydrocarbon with a single bond between two carbon atoms. The bond order between the carbon atoms in ethane is 1. The carbon-carbon bond length in ethane is longer than that in ethene and ethyne because it is a single bond.

Conclusion:
From the given options, ethyne (option c) has the shortest carbon-carbon bond length. This is because ethyne has a triple bond between the carbon atoms, which has the highest bond order among the given options. The bond length decreases as the bond order increases, so ethyne has the shortest carbon-carbon bond length.