Final answer:
The synapomorphy of primates relative to nonprimate mammals is the post-orbital bar, a skeletal feature that provides support around the eye socket.
Step-by-step explanation:
The synapomorphy of primates relative to nonprimate mammals is c. Post-orbital bar. A synapomorphy is a characteristic present in an ancestral species and shared exclusively by its evolutionary descendants. In primates, the presence of a post-orbital bar is a unique skeletal feature that supports and protects the eyes by providing a bony cup around the eye socket. This differs from the traits listed in the other options: a) Laterally-facing orbits are not a characteristic of primates, which tend to have forward-facing eyes; b) Claws on fingers and toes are more common in non-primate mammals, while primates usually have nails; and d) Large brains are characteristic of primates, but not exclusively so, as other non-primate mammals can also have relatively large brains.