What artery supplies the chin/jaw region of the head with blood?

The artery that supplies the chin and jaw region of the head with blood is the facial artery which is a branch of the external carotid artery. All blood from the head arises from the common carotid artery wherein it is divided to internal carotid artery (major blood supply of the brain along with the basilar artery on the posterior side) and external carotid artery (major blood supply of the head other than the brain).

The external carotid artery has 8 major branches (from inferior to superior): (1) superior thyroid artery, (2) ascending pharyngeal artery, (3) lingual artery, (4) facial artery, (5) occipital artery, (6) posterior auricular artery, (7) maxillary artery, and (6) superficial temporal artery. 

Attached is a simplified photo of the branches of the external carotid artery.

The answer is option b.