$$ \begin{aligned} \frac{7}{3} &= -\frac{1}{2}v+2+\frac{12}{3}&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6\cdot\frac{7}{3} &= -6 \cdot \frac{1}{2}v+6\cdot2+6\cdot\frac{12}{3}&& \text{cancel out the denominators} \\[1 em]14 &= -3v+12+24&& \text{simplify right side} \\[1 em]14 &= -3v+36&& \text{ swap the left and right side of the equation } \\[1 em]-3v+36 &= 14&& \text{ move 36 to the right } \\[1 em]-3v &= 14-36&& \\[1 em]-3v &= -22&& \text{ divide both sides by $ -3 $ } \\[1 em]v &= \frac{-22}{-3}&& \\[1 em]v &= \frac{22}{3}&& \\[1 em] \end{aligned} $$

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