Step 1: The concept of adult neurogenesis.
The mammalian central nervous system was long thought to be post-mitotic, but two niches retain neural stem cells capable of producing new neurons throughout adult life.
Step 2: The two recognised niches.
These are (a) the subgranular zone of the dentate gyrus of the hippocampus, which generates new granule-cell neurons important for learning and memory, and (b) the subventricular zone of the lateral ventricles, which feeds the rostral migratory stream to the olfactory bulb.
Step 3: Apply to the options.
The dentate gyrus is the classic answer and the only listed site of ongoing adult neurogenesis.
Step 4: Why the others are wrong.
The ventral spinal cord, substantia nigra (dopaminergic; its loss causes Parkinson disease and is not replenished) and locus ceruleus (noradrenergic) do not generate new neurons in the adult — their neuronal loss is permanent.
Key fact: Adult neurogenesis occurs in the dentate gyrus (hippocampus) and the subventricular zone.