Explanation

Let the numbers be n and n+2. Then 1/n + 1/(n+2) = 7/24 gives (2n+2)/(n(n+2)) = 7/24, i.e. 7n² − 34n − 48 = 0. Solving, n = 6 (the other root is negative), so the numbers are 6 and 8 with sum 14. Hence option C.