By what number should

Let the other number that should be multiplied with $\frac{-3}{4}$ to produce $\frac{2}{3}$ be $\mathrm{x}$.

$\therefore \mathrm{x} \times \frac{-3}{4}=\frac{2}{3}$

or $\mathrm{x}=\frac{2}{3} \div \frac{-3}{4}$

or $\mathrm{x}=\frac{2}{3} \times \frac{4}{-3}$

or $x=\frac{-8}{9}$

Thus, the number is $\frac{-8}{9}$.