I mean, colloquially, those places are on the other "side" of the world. If we think of what the other "side" means when talking about a sphere that rotates about an axis, the other "side" makes people think of the other "vertical" hemisphere when sliced along the rotational axis.

From a North American standpoint, take a city like Denver at 105 deg W. If you centre a vertical hemisphere over that longitude, then that hemisphere's borders would be at 90 deg either way. So from 15 deg W to "195 deg W" (15 deg E).

This ends up being a point off the west coast of the UK in line with the western coast of Africa all the way around to east of Japan.

While this is a technical definition I just made up, it sort of aligns with what people mean when they say "other side of the world".