We are given that AOF is an equilateral triangle. In an equilateral triangle, all three sides are equal and
therefore the perimeter of the triangle equals (number of sides) × (side length) = 3AF (where AF is one side of the equilateral triangle). Now, we are given that the perimeter of ΔAOF is 2a. Hence, 3AF = 2a, or
AF = 2a/3.
We are given that ABCDEF is a regular hexagon. In a regular hexagon, all six sides are equal and therefore
the perimeter of the hexagon equals (number of sides) × (side length) = 6AF (where AF is also one side of
the hexagon). Substituting AF = 2a/3 into this formula yields 6AF = 6(2a/3) = 4a.
The answer is (C).