imc

First look at the two cousins' ages that multiply to $24$. Since the ages must be single-digit, the ages must either be $3\text{ and }8$ or $4\text{ and }6.$ Next, look at the two cousins' ages that multiply to $30$. Since the ages must be single-digit, the only ages that work are $5\text{ and }6.$ Remembering that all the ages must all be distinct, the only solution that works is when the ages are $3,8$ and $5,6$. We are required to find the sum of the ages, which is $$3+8+5+6=\boxed{22}.$$