1. **State the problem:** Solve the equation $$4(x - 2) + 2x = -32$$ for $x$. 2. **Apply the distributive property:** Multiply 4 by each term inside the parentheses. $$4 \times x - 4 \times 2 + 2x = -32$$ which simplifies to $$4x - 8 + 2x = -32$$ 3. **Combine like terms:** Add $4x$ and $2x$. $$6x - 8 = -32$$ 4. **Isolate the term with $x$:** Add 8 to both sides. $$6x - 8 + 8 = -32 + 8$$ which simplifies to $$6x = -24$$ 5. **Solve for $x$:** Divide both sides by 6. $$\frac{6x}{\cancel{6}} = \frac{-24}{\cancel{6}}$$ which simplifies to $$x = -4$$ **Final answer:** $$x = -4$$