The product of two rational numbers is

Let the other number be $\mathrm{x}$.

$\therefore \mathrm{x} \times \frac{-4}{15}=\frac{-8}{9}$

or $\mathrm{x}=\frac{-8}{9} \div \frac{-4}{15}$

or $\mathrm{x}=\frac{-8}{9} \times \frac{15}{-4}$

or $\mathrm{x}=\frac{10}{3}$

Thus, the other number is $\frac{10}{3}$.