$$ \begin{aligned} \frac{4}{3}x-\frac{2}{3} &= 6x-\frac{5}{4}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{4}{3}x-12\cdot\frac{2}{3} &= 12\cdot6x-12\cdot\frac{5}{4}&& \text{cancel out the denominators} \\[1 em]16x-8 &= 72x-15&& \text{move the $ \color{blue}{ 72x } $ to the left side and $ \color{blue}{ -8 }$ to the right} \\[1 em]16x-72x &= -15+8&& \text{simplify left and right hand side} \\[1 em]-56x &= -7&& \text{ divide both sides by $ -56 $ } \\[1 em]x &= \frac{-7}{-56}&& \\[1 em]x &= \frac{1}{8}&& \\[1 em] \end{aligned} $$

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