Interview riddle

On the Mathematics chat we were recently talking about the following problem @Chris’ssis had to solve during an interview :

We have not managed to solve it so far, all we know is the solution (which was given after we had given up) :

$224$

How do we find this solution ?

To compute $a \times b$, take the numerator of $\dfrac{ab^2}{6}$ after simplification of the fraction.