1. **State the problem:** Solve the equation $6 + 2x = x - 6$ for $x$. 2. **Write down the equation:** $$6 + 2x = x - 6$$ 3. **Isolate the variable terms on one side:** Subtract $x$ from both sides: $$6 + 2x - x = x - 6 - x$$ which simplifies to $$6 + x = -6$$ 4. **Isolate the constant term:** Subtract 6 from both sides: $$6 + x - 6 = -6 - 6$$ which simplifies to $$x = -12$$ 5. **Final answer:** $$x = -12$$ This means the value of $x$ that satisfies the equation is $-12$.