1. **State the problem:** Solve the inequality $$-2(-3x + 2) \neq 20$$. 2. **Apply the distributive property:** Multiply $$-2$$ by each term inside the parentheses. $$-2 \times -3x = 6x$$ $$-2 \times 2 = -4$$ So the inequality becomes: $$6x - 4 \neq 20$$ 3. **Isolate the variable term:** Add 4 to both sides to move the constant term. $$6x - 4 + 4 \neq 20 + 4$$ $$6x \neq 24$$ 4. **Solve for $$x$$:** Divide both sides by 6. $$\frac{6x}{\cancel{6}} \neq \frac{24}{\cancel{6}}$$ $$x \neq 4$$ 5. **Interpretation:** The solution means $$x$$ can be any real number except 4. **Final answer:** $$x \neq 4$$