1. **State the problem:** Solve the equation $-2(x+6)=24$ for $x$. 2. **Use the distributive property:** Multiply $-2$ by each term inside the parentheses. $$-2(x+6) = -2 \times x + (-2) \times 6 = -2x - 12$$ So the equation becomes: $$-2x - 12 = 24$$ 3. **Isolate the term with $x$:** Add 12 to both sides to cancel $-12$. $$-2x - 12 + 12 = 24 + 12$$ $$-2x = 36$$ 4. **Solve for $x$:** Divide both sides by $-2$. $$\cancel{-2}x = \frac{36}{\cancel{-2}}$$ $$x = -18$$ 5. **Final answer:** $x = -18$. This means when $x$ is $-18$, the original equation holds true.