$$ \begin{aligned} \frac{1}{2}(12g+8) &= 0&& \text{simplify left side} \\[1 em]\frac{12g+8}{2} &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2 \cdot \frac{12g+8}{2} &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]12g+8 &= 0&& \text{ move the constants to the right } \\[1 em]12g &= -8&& \text{ divide both sides by $ 12 $ } \\[1 em]g &= -\frac{8}{12}&& \\[1 em]g &= -\frac{2}{3}&& \\[1 em] \end{aligned} $$

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