$$ \begin{aligned} \frac{1}{4}(x-2)+4 &= 12&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{1}{4}(x-2)+4\cdot4 &= 4\cdot12&& \text{cancel out the denominators} \\[1 em]x-2+16 &= 48&& \text{simplify left side} \\[1 em]x+14 &= 48&& \text{ move 14 to the right } \\[1 em]x &= 48-14&& \\[1 em]x &= 34&& \\[1 em]x &= 34&& \\[1 em] \end{aligned} $$

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