**Core Concept**
The sensory supply of the palate is a complex process involving multiple cranial nerves. The palate is divided into two main parts: the anterior two-thirds, which is primarily supplied by the trigeminal nerve, and the posterior one-third, which is supplied by the glossopharyngeal nerve. This division is crucial for understanding the sensory innervation of the palate.

**Why the Correct Answer is Right**
The hypoglossal nerve (Cranial Nerve XII) is primarily responsible for motor control of the tongue, specifically the extrinsic and intrinsic muscles. It does not contribute to the sensory innervation of the palate. In contrast, the facial nerve (Cranial Nerve VII) supplies taste to the anterior two-thirds of the tongue and also carries some sensory fibers to the palate, particularly from the anterior portion. The glossopharyngeal nerve (Cranial Nerve IX) is responsible for the sensory innervation of the posterior one-third of the tongue and the palate. The maxillary division of the trigeminal nerve (V2) supplies the anterior two-thirds of the palate with sensory fibers.

**Why Each Wrong Option is Incorrect**
**Option A:** The facial nerve does contribute to the sensory innervation of the palate, making it an incorrect choice.
**Option C:** The glossopharyngeal nerve is indeed responsible for the sensory innervation of the posterior one-third of the palate, making it an incorrect choice.
**Option D:** The maxillary division of the trigeminal nerve does supply the anterior two-thirds of the palate, making it an incorrect choice.

**Clinical Pearl / High-Yield Fact**
When examining a patient with a suspected lesion affecting the palate, it is essential to remember the distinct sensory innervation patterns of the anterior and posterior portions of the palate. This knowledge can aid in localizing the lesion and guiding further diagnostic and therapeutic interventions.

**✓ Correct Answer: B. Hypoglossal nerve**