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

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