Patient s. m. is able to recognize the emotions of happiness, sadness, and disgust portrayed in photographs, but has selective difficulty identifying fear correction. which brain region has probably suffered damage in this patient?

That would be the amygdala.

The amygdala It's located above the brain stem, in the medial temporal lob.
If bilateral damage in the  amygdala occurs, it will affect the recognition of fear because its the center of this process. Basically the amygdala will send a message to other parts of the brain, saying "pay attention!"

Most likely the region that has suffered damage is the Amygdala. Its primary function is in the regulation of human emotions such as fear, rage, aggression and other strong emotions. Patient s.m's ability to recognize some emotions but failure to process others is probably attributed to some damage to this area of the brain.