$$ \begin{aligned} \frac{t-6}{6} &= \frac{t+7}{7}&& \text{multiply ALL terms by } \color{blue}{ 42 }. \\[1 em]42 \cdot \frac{t-6}{6} &= 42 \cdot \frac{t+7}{7}&& \text{cancel out the denominators} \\[1 em]7t-42 &= 6t+42&& \text{move the $ \color{blue}{ 6t } $ to the left side and $ \color{blue}{ -42 }$ to the right} \\[1 em]7t-6t &= 42+42&& \text{simplify left and right hand side} \\[1 em]t &= 84&& \\[1 em]t &= 84&& \\[1 em] \end{aligned} $$

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