hi can someone please explain the solution to me please, thanks
Good! I presume that you realized from idbutt's picture that the if we take the distance from the center to a vertex of the outer hexagon to be 1, then the distance from the center to the middle of a side of that hexagon is . And that is where the circle touches the hexagon so is a vertex of the inner hexagon. Since those are "equivalent" distances, the ratio of the areas is the square of the ratio of those distances: .