$\dfrac{4}{9} \div\ ? = \dfrac{-8}{15}$

1. $\dfrac{-32}{45}$

2. $\dfrac{-8}{5}$

3. $\dfrac{-9}{10}$

4. $\dfrac{-5}{6}$

Let the required rational number be $x$.

According to the given condition,

$\Rightarrow \dfrac{4}{9} \div x = \dfrac{-8}{15} \\[1em] \Rightarrow x = \dfrac{4}{9} \div \dfrac{-8}{15} \\[1em] \Rightarrow x = \dfrac{4}{9} \times \dfrac{15}{-8} \\[1em] \Rightarrow x = \dfrac{4 \times 15}{9 \times (-8)} \\[1em] \Rightarrow x = \dfrac{60}{-72} = \dfrac{-5}{6}$

Hence, Option 4 is the correct option.