$$3(2x-1) = \frac{1}{2}(x+6)$$

$$ \begin{aligned} 3(2x-1) &= \frac{1}{2}(x+6)&& \text{simplify left and right hand side} \\[1 em]6x-3 &= \frac{x+6}{2}&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot6x-2\cdot3 &= 2 \cdot \frac{x+6}{2}&& \text{cancel out the denominators} \\[1 em]12x-6 &= x+6&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ -6 }$ to the right} \\[1 em]12x-x &= 6+6&& \text{simplify left and right hand side} \\[1 em]11x &= 12&& \text{ divide both sides by $ 11 $ } \\[1 em]x &= \frac{12}{11}&& \\[1 em] \end{aligned} $$

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