The correct answer is $\boxed{\text{D}}$. Ethyne has the largest distance between two adjacent carbon atoms.
In ethane, the two carbon atoms are bonded by a single bond, which is a sigma bond. A sigma bond is a covalent bond that is formed by the overlap of two atomic orbitals along the internuclear axis. The overlap of the two atomic orbitals in ethane is relatively small, which results in a short bond length.
In ethene, the two carbon atoms are bonded by a double bond, which is a sigma bond and a pi bond. A pi bond is a covalent bond that is formed by the overlap of two parallel atomic orbitals above and below the internuclear axis. The overlap of the two atomic orbitals in ethene is greater than the overlap of the two atomic orbitals in ethane, which results in a longer bond length.
In ethyne, the two carbon atoms are bonded by a triple bond, which is a sigma bond and two pi bonds. The overlap of the two atomic orbitals in ethyne is greater than the overlap of the two atomic orbitals in ethene, which results in a longer bond length.
Therefore, the distance between two adjacent carbon atoms is largest in ethyne.