$$ \begin{aligned} \frac{2x-4}{2x+6} &= \frac{5}{6}&& \text{multiply ALL terms by } \color{blue}{ (2x+6)\cdot6 }. \\[1 em](2x+6)\cdot6 \cdot \frac{2x-4}{2x+6} &= (2x+6)\cdot6\cdot\frac{5}{6}&& \text{cancel out the denominators} \\[1 em]12x-24 &= 10x+30&& \text{move the $ \color{blue}{ 10x } $ to the left side and $ \color{blue}{ -24 }$ to the right} \\[1 em]12x-10x &= 30+24&& \text{simplify left and right hand side} \\[1 em]2x &= 54&& \text{ divide both sides by $ 2 $ } \\[1 em]x &= \frac{54}{2}&& \\[1 em]x &= 27&& \\[1 em] \end{aligned} $$

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