1. **State the problem:** Solve the cubic equation $$ (3x - 4)^3 = 8 $$ 2. **Recall the formula:** To solve an equation of the form $$ (a)^3 = b $$, take the cube root of both sides: $$ a = \sqrt[3]{b} $$ 3. **Apply the cube root:** $$ (3x - 4)^3 = 8 \implies 3x - 4 = \sqrt[3]{8} $$ 4. **Evaluate the cube root:** $$ \sqrt[3]{8} = 2 $$ 5. **Solve for x:** $$ 3x - 4 = 2 $$ $$ 3x = 2 + 4 $$ $$ 3x = 6 $$ $$ x = \frac{6}{3} $$ 6. **Cancel common factors:** $$ x = \frac{\cancel{6}}{\cancel{3}} = 2 $$ **Final answer:** $$ x = 2 $$