Answer: Hello there!
A regular hexagon has 6 equal sides, so if you want to see the symetri angles, you need to see:
A = n*360/6 where n can be 0,1,2,3,4,5,6
then
A₀ = 0°
A₁ = 360°/6 = 60°
A₂ = 120°
A₃ = 180°
A₄ = 240°
A₅ = 300°
A₆ = 360°
discarding A₀ = 0° ( because this is not a rotation) You have 6 angles for symmetrical rotation, so the order of rotational symmetry is is 6.