$$ \begin{aligned} \frac{3}{2} &= \frac{6}{x}-4&& \text{multiply ALL terms by } \color{blue}{ 2x }. \\[1 em]2x\cdot\frac{3}{2} &= 2x\cdot\frac{6}{x}-2x\cdot4&& \text{cancel out the denominators} \\[1 em]3x &= 12-8x&& \text{move the $ \color{blue}{ -8x } $ to the left side} \\[1 em]3x+8x &= 12&& \text{simplify left side} \\[1 em]11x &= 12&& \text{ divide both sides by $ 11 $ } \\[1 em]x &= \frac{12}{11}&& \\[1 em] \end{aligned} $$

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