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

$$ \begin{aligned} \frac{x+3}{2}-\frac{x}{4} &= \frac{4}{3}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{x+3}{2}-12\frac{x}{4} &= 12\cdot\frac{4}{3}&& \text{cancel out the denominators} \\[1 em]6x+18-3x &= 16&& \text{simplify left side} \\[1 em]3x+18 &= 16&& \text{ move 18 to the right } \\[1 em]3x &= 16-18&& \\[1 em]3x &= -2&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= -\frac{2}{3}&& \\[1 em] \end{aligned} $$

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