Final answer:
The nerve that may have been damaged in the patient with the mandibular fracture is the Buccal branch of mandibular nerve (long buccal nerve).
Step-by-step explanation:
The nerve that may have been damaged in the patient with the mandibular fracture is the Buccal branch of mandibular nerve (long buccal nerve). The buccal branch of the mandibular nerve provides sensory innervation to the buccal mucosa, lower lip, and skin of the lower face. Damage to this nerve can result in numbness or altered sensation in the affected areas.