Hi Alice. Since tan(x) is defined by opposite over adjacent, you can find the hypotenuse R using Pythagorean Theorem: R = sqrt(7^2 + 24^2). This enables you to find cos(x) = adjacent/hypotenuse = 7/R. Finally since cos(2x) = 2cos^2(x) minus 1, you can find cos(2x) by substituting the result you get for cos(x) into the formula for cos(2x).
Since tan(x) = 24/7 which is larger than 1, the angle x is between 45 and 90 deg which means that 2x is between 90 and 180. This means that angle 2x is in the second quadrant so cos(2x) must be negative.
Hope this helps.