**Core Concept**
The question is testing the student's knowledge of the extraocular muscles and their innervation. The inability to look downward and laterally is a specific movement that can be impaired due to damage to a particular cranial nerve. This cranial nerve is responsible for the motor supply to one of the extraocular muscles.

**Why the Correct Answer is Right**
The correct answer is related to the innervation of the inferior oblique muscle. The inferior oblique muscle is responsible for the movement of looking downward and laterally. The cranial nerve that innervates the inferior oblique muscle is the **oculomotor nerve (CN III)**. However, the oculomotor nerve also innervates other muscles and has a broader range of functions. The more specific association with the inferior oblique muscle is with the **trochlear nerve (CN IV)**. The trochlear nerve is the thinnest and longest cranial nerve, and it innervates the **superior oblique muscle** primarily, but the **trochlear nerve also innervates the inferior oblique muscle**. The superior oblique muscle is responsible for the movement of looking downward and medially, but its innervation is not the correct answer in this case. However, **the trochlear nerve (CN IV)** is responsible for the movement of looking downward and laterally due to the function of the superior oblique muscle.

**Why Each Wrong Option is Incorrect**
* **Option A:** The **abducens nerve (CN VI)** is responsible for the innervation of the lateral rectus muscle, which is responsible for the movement of looking laterally, but not downward.
* **Option C:** The **trigeminal nerve (CN V)** is responsible for the sensory supply to the face, including the eye, but not the motor supply to the extraocular muscles.
* **Option D:** The **facial nerve (CN VII)** is responsible for the motor supply to the muscles of facial expression, but not the extraocular muscles.

**Clinical Pearl / High-Yield Fact**
The trochlear nerve (CN IV) is the thinnest and longest cranial nerve, and it is the only cranial nerve that decussates (crosses over) before exiting the brainstem.

**Correct Answer: B. The trochlear nerve (CN IV)**