Final answer:
The neurons projecting to the posterior pituitary originate from the supraoptic and paraventricular nuclei of the hypothalamus, responsible for the production and release of hormones like oxytocin and ADH.
Step-by-step explanation:
The neurons that project to the posterior pituitary (neurohypophysis) come from the supraoptic and paraventricular nuclei of the hypothalamus. These nuclei produce important hormones like oxytocin and antidiuretic hormone (ADH), also known as vasopressin. These hormones are then transported along the axons of these neurons down the infundibulum to the posterior pituitary, where they are stored and eventually released into the bloodstream.