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

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