**Core Concept**
Thyroglossal duct cysts (TDCs) are congenital anomalies resulting from remnants of the thyroglossal duct, which normally involutes during embryonic development. These cysts can be located along the midline of the neck, from the foramen cecum at the base of the tongue to the hyoid bone.

**Why the Correct Answer is Right**
The thyroglossal duct cysts move with protrusion of the tongue due to the remnants of the thyroglossal duct, which are attached to the foramen cecum at the base of the tongue. The foramen cecum is a small opening at the back of the tongue that marks the site of the embryonic thyroglossal duct. As the tongue is protruded, the cyst is pulled forward due to its attachment to this duct. This characteristic movement is a diagnostic clue for thyroglossal duct cysts.

**Why Each Wrong Option is Incorrect**
* **Option B:** The hyoid bone is a bony structure that supports the tongue, but it is not directly attached to the thyroglossal duct remnants. While the thyroglossal duct cyst may be located near the hyoid bone, its movement with tongue protrusion is due to its attachment to the foramen cecum.
* **Option C:** The pharynx is a muscular tube that carries food from the mouth to the esophagus, but it is not directly related to the movement of thyroglossal duct cysts with tongue protrusion.
* **Option D:** The sternocleidomastoid muscle is a muscle of the neck that assists in neck flexion and rotation, but it is not directly attached to the thyroglossal duct remnants and is not responsible for the movement of thyroglossal duct cysts with tongue protrusion.

**Clinical Pearl / High-Yield Fact**
Thyroglossal duct cysts are congenital anomalies that can present at any age, but they are most commonly diagnosed in children. A key diagnostic feature is the movement of the cyst with tongue protrusion, which is due to its attachment to the foramen cecum at the base of the tongue.

**Correct Answer: A. Foramen cecum.**