The largest degree of rotation, excluding 360 degrees, that would turn a regular hexagon onto itself is 300 degrees.
This is because a regular hexagon has rotational symmetries at 0 degrees, 60 degrees, 120 degrees, 180 degrees, 240 degrees, 300 degrees, and 360 degrees. The largest rotation that results in the hexagon appearing unchanged, aside from 360 degrees, is 300 degrees.