$$ \begin{aligned} 2-\frac{12}{x} &= 6&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot2-x\cdot\frac{12}{x} &= x\cdot6&& \text{cancel out the denominators} \\[1 em]2x-12 &= 6x&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ -12 }$ to the right} \\[1 em]2x-6x &= 12&& \text{simplify left side} \\[1 em]-4x &= 12&& \text{ divide both sides by $ -4 $ } \\[1 em]x &= -\frac{12}{4}&& \\[1 em]x &= -3&& \\[1 em] \end{aligned} $$

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