A patient with an injured facial nerve (CN VII) would have difficulty with which action?

The correct response highlights the essential function of the facial nerve (cranial nerve VII), which is primarily responsible for the motor control of the muscles of facial expression. An injury to this nerve would severely impact the ability to perform movements associated with facial expressions, such as grinning or grimacing.

Facial expressions are controlled by the muscles innervated by the facial nerve, and any dysfunction could lead to weakness or paralysis of these muscles on the affected side of the face. Thus, actions that involve the use of these muscles, like grinning or grimacing, would be particularly difficult for the patient.

In contrast, extending the head, elevating the mandible, or flexing the wrist involves different muscles and nerves that are not affected by damage to the facial nerve. For instance, extending the head primarily utilizes the sternocleidomastoid and trapezius muscles, while elevating the mandible involves the muscles of mastication, specifically innervated by the trigeminal nerve (CN V). Flexing the wrist involves the muscles of the forearm that are controlled by the radial, median, and ulnar nerves. Thus, those actions would be unaffected by an injury to the facial nerve.