$$ \begin{aligned} \frac{2x\cdot3-4x\cdot2+8x-2}{x}+4 &= 0&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x \cdot \frac{2x\cdot3-4x\cdot2+8x-2}{x}+x\cdot4 &= x\cdot0&& \text{cancel out the denominators} \\[1 em]6x-2+4x &= 0&& \text{simplify left side} \\[1 em]10x-2 &= 0&& \text{ move the constants to the right } \\[1 em]10x &= 2&& \text{ divide both sides by $ 10 $ } \\[1 em]x &= \frac{2}{10}&& \\[1 em]x &= \frac{1}{5}&& \\[1 em] \end{aligned} $$

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