1. **State the problem:** Simplify the expression $\frac{4}{5} + \frac{2}{3} \times 4$. 2. **Recall the order of operations:** Multiplication must be done before addition. 3. **Calculate the multiplication first:** $$\frac{2}{3} \times 4 = \frac{2}{3} \times \frac{4}{1} = \frac{2 \times 4}{3 \times 1} = \frac{8}{3}$$ 4. **Rewrite the expression:** $$\frac{4}{5} + \frac{8}{3}$$ 5. **Find a common denominator:** The denominators are 5 and 3, so the least common denominator is 15. 6. **Convert each fraction:** $$\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}$$ $$\frac{8}{3} = \frac{8 \times 5}{3 \times 5} = \frac{40}{15}$$ 7. **Add the fractions:** $$\frac{12}{15} + \frac{40}{15} = \frac{12 + 40}{15} = \frac{52}{15}$$ 8. **Final answer:** $$\frac{52}{15}$$ which is an improper fraction and can be left as is or converted to a mixed number: $$3 \frac{7}{15}$$