We can also understand the bond length with the help of the $s$ character.

Higher the $s$-character lesser is the bond length.

This is because higher $s$ character implies that the electrons that are bonded pairs are closely held together, thus making the bond length small as well as strong.

Hybridisation of $C _2 H _6$ is $sp ^3$

The $s$ character in $C _2 H _6$ (Ethane) is: $\frac{1}{4} \times 100=25 \,\%$ which is the least amongst the other given compounds.

Therefore the $C - H$ bond length of $C _2 H _6$ is the longest.

Hence it is the correct option.