Final answer:
Dan's inability to recognize familiar faces after a brain trauma suggests damage to the anterior fusiform gyrus of the temporal lobe, which is associated with facial recognition and possibly to the hippocampus that is involved in memory formation.
Step-by-step explanation:
If Dan can no longer remember the faces of people he knew after a brain injury, it is likely that he has incurred damage to his temporal lobe, particularly the region known as the anterior fusiform gyrus. This area is associated with the process of recognizing faces, a condition known as prosopagnosia when damaged or dysfunctional. In addition, the hippocampus may also be affected, as it plays a critical role in forming new memories and connecting them to familiar visual stimuli.
The part of the brain that is most likely damaged in Dan's case is the temporal lobe. Specifically, the anterior fusiform gyrus in the temporal lobe is responsible for facial recognition. When this region is damaged, it can result in a condition called prosopagnosia, which is the inability to recognize faces of people you know.