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 $\displaystyle \sqrt{3}/2$. 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: $\displaystyle \left(\frac{1}{\sqrt{3}/2}\right)^2= \frac{1}{3/4}= \frac{4}{3}$.