$$ \begin{aligned} 4(\frac{1}{3}t+\frac{1}{2}) &= 0&& \text{simplify left side} \\[1 em]4(\frac{t}{3}+\frac{1}{2}) &= 0&& \\[1 em]4 \cdot \frac{2t+3}{6} &= 0&& \\[1 em]\frac{8t+12}{6} &= 0&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{8t+12}{6} &= 6\cdot0&& \text{cancel out the denominators} \\[1 em]8t+12 &= 0&& \text{ move the constants to the right } \\[1 em]8t &= -12&& \text{ divide both sides by $ 8 $ } \\[1 em]t &= -\frac{12}{8}&& \\[1 em]t &= -\frac{3}{2}&& \\[1 em] \end{aligned} $$

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