$$3-\frac{2}{x} = 8$$

$$ \begin{aligned} 3-\frac{2}{x} &= 8&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot3-x\cdot\frac{2}{x} &= x\cdot8&& \text{cancel out the denominators} \\[1 em]3x-2 &= 8x&& \text{move the $ \color{blue}{ 8x } $ to the left side and $ \color{blue}{ -2 }$ to the right} \\[1 em]3x-8x &= 2&& \text{simplify left side} \\[1 em]-5x &= 2&& \text{ divide both sides by $ -5 $ } \\[1 em]x &= -\frac{2}{5}&& \\[1 em] \end{aligned} $$

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