Final answer:
A 120-degree counterclockwise rotation is the correct answer as it is a multiple of the 60° angle that represents the sixfold symmetry of a hexagon, carrying it onto itself.
Step-by-step explanation:
The angles of rotation that will carry a regular hexagon onto itself are 60°, 120°, 180°, 240°, 300°, and 360°. Among the given options, only a rotation of 120 degrees counterclockwise will carry a hexagon onto itself. This is because a regular hexagon has six sides and therefore sixfold symmetry; each side represents a fraction of the 360° full rotation, which is 360°/6 = 60°. Therefore, any multiple of this angle will map the hexagon onto itself. Option C, a 120 degree counterclockwise rotation, is such a multiple (2 × 60°) and is correct.