$$ \begin{aligned} 2x-\frac{3}{6} &= x+\frac{4}{1}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot2x-6\cdot\frac{3}{6} &= 6x+6\cdot\frac{4}{1}&& \text{cancel out the denominators} \\[1 em]12x-3 &= 6x+24&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ -3 }$ to the right} \\[1 em]12x-6x &= 24+3&& \text{simplify left and right hand side} \\[1 em]6x &= 27&& \text{ divide both sides by $ 6 $ } \\[1 em]x &= \frac{27}{6}&& \\[1 em]x &= \frac{9}{2}&& \\[1 em] \end{aligned} $$

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