$$ \begin{aligned} 4x+12 &= -2(x-4)&& \text{simplify right side} \\[1 em]4x+12 &= -(2x-8)&& \\[1 em]4x+12 &= -2x+8&& \text{move the $ \color{blue}{ -2x } $ to the left side and $ \color{blue}{ 12 }$ to the right} \\[1 em]4x+2x &= 8-12&& \text{simplify left and right hand side} \\[1 em]6x &= -4&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= -\frac{4}{6}&& \\[1 em]x &= -\frac{2}{3}&& \\[1 em] \end{aligned} $$

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