**Core Concept**
The stylohyoid muscle is a small muscle of the neck that plays a crucial role in the movement of the hyoid bone. It is innervated by a specific branch of the cranial nerve that is responsible for the motor control of various muscles in the neck.

**Why the Correct Answer is Right**
The stylohyoid muscle is supplied by the facial nerve, specifically its stylomastoid branch. This branch arises from the facial nerve after it exits the stylomastoid foramen and before it reaches the parotid gland. The stylomastoid branch then descends through the stylomastoid foramen and innervates the stylohyoid muscle, as well as the posterior belly of the digastric muscle. The innervation of the stylohyoid muscle by the facial nerve is essential for its function in elevating the hyoid bone during swallowing.

**Why Each Wrong Option is Incorrect**
**Option A:**
This option is incorrect because the accessory nerve (cranial nerve XI) primarily supplies the sternocleidomastoid and trapezius muscles, which are involved in shoulder movement.

**Option B:**
This option is incorrect because the hypoglossal nerve (cranial nerve XII) primarily supplies the muscles of the tongue, which are involved in tongue movement and speech.

**Option C:**
This option is incorrect because the vagus nerve (cranial nerve X) primarily supplies the laryngeal muscles and the pharyngeal muscles involved in swallowing.

**Clinical Pearl / High-Yield Fact**
The facial nerve is responsible for the motor control of various muscles in the face, including the muscles of facial expression, as well as the stylohyoid and posterior belly of the digastric muscles in the neck.

**Correct Answer: D. The stylohyoid muscle is supplied by the facial nerve.