Each cranial nerve has one main job, and only one of these four numbers is wired to the heart at all, which makes this mostly a matter of recalling what each nerve supplies.
- IX: Supplies taste and the gag reflex from the throat region, no cardiac fibers involved.
- VII: Runs the muscles behind facial expressions and a couple of glands, again with no connection to the heart.
- X: The vagus nerve travels far beyond the head and neck, sending parasympathetic branches down to the heart, lungs, and gut. At the heart specifically, it slows the sinoatrial node's own firing rate by releasing acetylcholine there, which is exactly the kind of heartbeat regulation the question is asking about.
- VIII: Dedicated entirely to hearing and balance signals from the inner ear, with nothing to do with the heart.
The vagus nerve's unusually long reach into the chest and abdomen is what lets it, and only it among these four, regulate the heartbeat. The correct answer is X.