$$\frac{x+2}{3} = \frac{2x-4}{2}$$

$$ \begin{aligned} \frac{x+2}{3} &= \frac{2x-4}{2}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{x+2}{3} &= 6 \cdot \frac{2x-4}{2}&& \text{cancel out the denominators} \\[1 em]2x+4 &= 6x-12&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ 4 }$ to the right} \\[1 em]2x-6x &= -12-4&& \text{simplify left and right hand side} \\[1 em]-4x &= -16&& \text{ divide both sides by $ -4 $ } \\[1 em]x &= \frac{-16}{-4}&& \\[1 em]x &= 4&& \\[1 em] \end{aligned} $$

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