$$\frac{x-4}{3} = \frac{-2-4x}{6}$$

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

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