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

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