1. **State the problem:** Simplify the expression $$\frac{2}{3} \times \frac{4}{5}$$. 2. **Recall the rule for multiplying fractions:** Multiply the numerators together and the denominators together. 3. **Apply the rule:** $$\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}$$ 4. **Check if the fraction can be simplified:** 8 and 15 have no common factors other than 1, so $$\frac{8}{15}$$ is already in simplest form. 5. **Final answer:** $$\frac{8}{15}$$