$$ \begin{aligned} \frac{4}{6}x-3x+\frac{8}{3} &= \frac{4}{3}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{4}{6}x-6\cdot3x+6\cdot\frac{8}{3} &= 6\cdot\frac{4}{3}&& \text{cancel out the denominators} \\[1 em]4x-18x+16 &= 8&& \text{simplify left side} \\[1 em]-14x+16 &= 8&& \text{ move 16 to the right } \\[1 em]-14x &= 8-16&& \\[1 em]-14x &= -8&& \text{ divide both sides by $ -14 $ } \\[1 em]x &= \frac{-8}{-14}&& \\[1 em]x &= \frac{4}{7}&& \\[1 em] \end{aligned} $$

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