John Gill Commentary Luke 4:31

"And he came down to Capernaum, a city of Galilee. And he was teaching them on the sabbath day:" — Luke 4:31 (ASV)

And came down to Capernaum
Which was, as Dr. Lightfoot thinks, sixteen miles or more from Nazareth; and Christ may be said to "come down" to it, because of the situation of Nazareth, which was upon an hill:

a city of Galilee :
of lower Galilee, near the sea of Galilee:

and taught them on the sabbath days :
that is, he went into the synagogue at Capernaum, on the sabbath days, whenever he was there, and taught the inhabitants, explained some passage or other in the Old Testament, as he had done at Nazareth and instructed them in the doctrines of the Gospel.