$$ \begin{aligned} \frac{1}{6}(4t-4) &= \frac{1}{12}(t+4)&& \text{simplify left and right hand side} \\[1 em]\frac{4t-4}{6} &= \frac{t+4}{12}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12 \cdot \frac{4t-4}{6} &= 12 \cdot \frac{t+4}{12}&& \text{cancel out the denominators} \\[1 em]8t-8 &= t+4&& \text{move the $ \color{blue}{ t } $ to the left side and $ \color{blue}{ -8 }$ to the right} \\[1 em]8t-t &= 4+8&& \text{simplify left and right hand side} \\[1 em]7t &= 12&& \text{ divide both sides by $ 7 $ } \\[1 em]t &= \frac{12}{7}&& \\[1 em] \end{aligned} $$

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