$$ \begin{aligned} 2+\frac{x}{6} &= 3 \cdot \frac{x}{8}&& \text{multiply ALL terms by } \color{blue}{ 24 }. \\[1 em]24\cdot2+24 \cdot \frac{x}{6} &= 24\cdot3 \cdot \frac{x}{8}&& \text{cancel out the denominators} \\[1 em]48+4x &= 9x&& \text{move the $ \color{blue}{ 9x } $ to the left side and $ \color{blue}{ 48 }$ to the right} \\[1 em]4x-9x &= -48&& \text{simplify left side} \\[1 em]-5x &= -48&& \text{ divide both sides by $ -5 $ } \\[1 em]x &= \frac{-48}{-5}&& \\[1 em]x &= \frac{48}{5}&& \\[1 em] \end{aligned} $$

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