1. We are asked to solve the division problem $\frac{8}{9} \div \frac{4}{15}$. 2. The formula for dividing fractions is: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$ This means we multiply the first fraction by the reciprocal of the second fraction. 3. Applying the formula: $$\frac{8}{9} \div \frac{4}{15} = \frac{8}{9} \times \frac{15}{4}$$ 4. Multiply the numerators and denominators: $$= \frac{8 \times 15}{9 \times 4} = \frac{120}{36}$$ 5. Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD). The GCD of 120 and 36 is 12: $$= \frac{\cancel{12} \times 10}{\cancel{12} \times 3} = \frac{10}{3}$$ 6. The final answer is an improper fraction: $$\boxed{\frac{10}{3}}$$