1. **State the problem:** Solve the equation $4 - 2x + 8 = -6$ for $x$. 2. **Combine like terms on the left side:** $4 + 8 = 12$, so the equation becomes: $$12 - 2x = -6$$ 3. **Isolate the term with $x$:** Subtract 12 from both sides: $$12 - 2x - 12 = -6 - 12$$ $$-2x = -18$$ 4. **Solve for $x$:** Divide both sides by $-2$: $$x = \frac{-18}{-2} = 9$$ 5. **Final answer:** $$x = 9$$ This means the value of $x$ that satisfies the equation is 9.