The correct answer is the cranial nerve III, or answer B. This is also called the oculomotor nerve. The previous answer is correct on this point. As for the explanation, I’ll simply expand on what the other cranial nerves control. The second cranial nerve (answer A) controls the transmission of information from the eye to the retina; it helps you see, basically.
The sixth cranial nerve (answer C) is formally known as the abducens nerve. It controls the outward gaze of a human being. This is often the nerve that causes double vision when it’s damaged. Finally, the seventh cranial nerve (answer D) controls facial expressions. For this reason, it’s called the facial nerve. For brainiacs of the brain, it emerges from the brain between the pons and medulla.
Rationale: B is the correct answer because Cranial nerve III (oculomotor) controls eyelid movement. A and D are distracters because you could be fooled that the optic (II) or facial (VII) nerves affect eyelid droop.
Source: Neuroscience: Fundamentals for Rehabilitation, Lundy-Ekman