A regular hexagon has rotational symmetry at various degrees. The largest degree of rotation, excluding 360°, that would turn a regular hexagon onto itself is 300°.
To explain further, a regular hexagon can be rotated by 60°, 120°, 180°, 240°, and 300° while still appearing the same. Therefore, the answer is:
A rotation of 300° would turn a regular hexagon onto itself.