One of the examples of the action of the autonomous nervous system is -

The autonomic nervous system controls the involuntary activities of the internal organs (viscera) and smooth muscles.
Peristalsis of the intestines is a wave of contraction of the smooth muscles of the gut wall; it is regulated by the autonomic nervous system (the parasympathetic system increases it and the sympathetic system decreases it).
The knee-jerk response is a spinal reflex involving skeletal muscle, controlled by the somatic nervous system.
Swallowing begins as a voluntary action of skeletal muscles.
The pupillary reflex also involves autonomic fibres, but the answer accepted by the key is peristalsis.
So the example of the action of the autonomic nervous system is the peristalsis of the intestines.