Final answer:
The 2nd-order neurons of the spinothalamic tract synapse in the ventral posterolateral (VPL) nucleus of the thalamus and then project their axons to the spinothalamic tract, which synapses in the postcentral gyrus of the cerebral cortex.
Step-by-step explanation:
The 2nd-order neurons of the spinothalamic tract synapse in the ventral posterolateral (VPL) nucleus of the thalamus. The name "spinothalamic" comes from this second neuron, which has its cell body in the spinal cord gray matter and connects to the thalamus.
Axons from these second neurons then decussate within the spinal cord and ascend to the brain and enter the thalamus, where each synapses with the third neuron in its respective pathway. The neurons in the thalamus then project their axons to the spinothalamic tract, which synapses in the postcentral gyrus of the cerebral cortex.