$$ \begin{aligned} \frac{x+2}{6} &= \frac{2x-10}{8}&& \text{multiply ALL terms by } \color{blue}{ 24 }. \\[1 em]24 \cdot \frac{x+2}{6} &= 24 \cdot \frac{2x-10}{8}&& \text{cancel out the denominators} \\[1 em]4x+8 &= 6x-30&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ 8 }$ to the right} \\[1 em]4x-6x &= -30-8&& \text{simplify left and right hand side} \\[1 em]-2x &= -38&& \text{ divide both sides by $ -2 $ } \\[1 em]x &= \frac{-38}{-2}&& \\[1 em]x &= 19&& \\[1 em] \end{aligned} $$

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