The mobility of free electrons is greater than that of holes because

The correct option is D They require lower energy to continue their motion.
When an electric field $E$ is applied over a piece of material, the electrons move at an average velocity known as the drift velocity $v_d$.

The electron mobility is $\mu$ then described as follows,

$v_d=\mu E$

Electrons need less energy to move because they encounter less resistance during their motion than holes.

Also, the free electrons are present in conduction band and the holes are present in valence band, so, the free electrons require lower energy to continue their motion.

So, electron mobility is often greater than hole mobility.

Hence, option $\left(D\right)$ is correct.