$$ \begin{aligned} \frac{6}{x}+2+\frac{1}{x}-2 &= -\frac{1}{x}\cdot2-4&& \text{multiply ALL terms by } \color{blue}{ x }. \\[1 em]x\cdot\frac{6}{x}+x\cdot2+x\cdot\frac{1}{x}-x\cdot2 &= -x \cdot \frac{1}{x}\cdot2-x\cdot4&& \text{cancel out the denominators} \\[1 em]6+2x+1-2x &= -2-4x&& \text{simplify left and right hand side} \\[1 em]6+2x+1-2x &= -4x-2&& \\[1 em]7 &= -4x-2&& \text{ swap the left and right side of the equation } \\[1 em]-4x-2 &= 7&& \text{ move -2 to the right } \\[1 em]-4x &= 7+2&& \\[1 em]-4x &= 9&& \text{ divide both sides by $ -4 $ } \\[1 em]x &= -\frac{9}{4}&& \\[1 em] \end{aligned} $$

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