1. **State the problem:** Solve the equation $$ (3x + 2)^{\frac{2}{5}} = 4 $$. 2. **Formula and rules:** To solve equations with fractional exponents, raise both sides to the reciprocal power to eliminate the fractional exponent. 3. **Isolate the term:** The term with the fractional exponent is already isolated. 4. **Raise both sides to the power of 5/2:** $$ \left((3x + 2)^{\frac{2}{5}}\right)^{\frac{5}{2}} = 4^{\frac{5}{2}} $$ 5. **Simplify the left side:** $$ (3x + 2)^{\cancel{\frac{2}{5} \times \frac{5}{2}}} = 4^{\frac{5}{2}} $$ $$ 3x + 2 = 4^{\frac{5}{2}} $$ 6. **Calculate the right side:** $$ 4^{\frac{5}{2}} = \left(4^{\frac{1}{2}}\right)^5 = (2)^5 = 32 $$ 7. **Solve for x:** $$ 3x + 2 = 32 $$ $$ 3x = 32 - 2 $$ $$ 3x = 30 $$ $$ x = \frac{30}{3} $$ 8. **Simplify the fraction:** $$ x = \frac{\cancel{30}}{\cancel{3}} = 10 $$ **Final answer:** $$ x = 10 $$