It is the only cranial nerve that arises from the brain posteriorly (near the back), establishing the longest pathway. This cranial nerve assists the eye as it is the smallest nerve.
Option A is incorrect. The vagus nerve is a very complex Xth cranial nerve. It has functions both sensorial and motor. The vagus nerve, of all the cranial nerves, has the longest path. It stretches from your head into your abdomen. It comes from the portion of your brainstem which is called the medulla.
Option B is incorrect. The abducens nerve (VIth cranial nerve) regulates another muscle, called the lateral rectal muscle, that is associated with eye movement. This muscle is involved in pushing the eyes outward. For example, use that to look to the left. The nerve, also called the abductive nerve, begins in your brainstem's pons area. It ends up in your eye socket, where it regulates the lateral rectus muscle.
Option C is incorrect. The facial nerve is the VIIth cranial nerve supplying functions both sensory and motor. The facial nerve has a very complicated course. It originates in your brainstem's pons region, where it has both the motor and the sensory root. The two nerves gradually merge into one another to form the facial nerve. The facial nerve branches further through smaller nerve fibers, both within and outside your skull, which trigger muscles and glands or provide sensory information.
Option D is correct. The trochlear nerve is the IVth cranial nerve connected. It is the smallest cranial nerve (by axon number), but it has the longest intracranial path. It's regulating the upper oblique muscle. This is the muscle responsible for the movement of the eyes upward, outwards, and inward.
So, the correct answer is Option D.
Note: The trochlear nerve is primarily a motor nerve, and the only cranial nerve to dorsally exit the brain. One muscle is supplied by the Trochlear Nerve: the superior oblique. The cell bodies that form the fourth cranial nerve are located in the trochlear nucleus, in the ventral part of the brainstem.