1. **Problem 1: Multiply the fractions** $\frac{2}{3} \times \frac{6}{5}$. 2. Use the multiplication rule for fractions: multiply numerators and denominators: $$\frac{2}{3} \times \frac{6}{5} = \frac{2 \times 6}{3 \times 5} = \frac{12}{15}$$ 3. Simplify $\frac{12}{15}$ by dividing numerator and denominator by their greatest common divisor (GCD), which is 3: $$\frac{12 \div 3}{15 \div 3} = \frac{4}{5}$$ 4. **Answer for Problem 1:** $\frac{4}{5}$. 5. **Problem 2: Divide the fractions** $\frac{3}{2} \div \frac{8}{5}$. 6. Use the division rule for fractions: multiply the first fraction by the reciprocal of the second: $$\frac{3}{2} \div \frac{8}{5} = \frac{3}{2} \times \frac{5}{8} = \frac{3 \times 5}{2 \times 8} = \frac{15}{16}$$ 7. $\frac{15}{16}$ is already in simplest form. 8. **Answer for Problem 2:** $\frac{15}{16}$.