$$-\frac{2}{3}+\frac{3}{4}+x = \frac{1}{4}$$

$$ \begin{aligned} -\frac{2}{3}+\frac{3}{4}+x &= \frac{1}{4}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]-12\cdot\frac{2}{3}+12\cdot\frac{3}{4}+12x &= 12\cdot\frac{1}{4}&& \text{cancel out the denominators} \\[1 em]-8+9+12x &= 3&& \text{simplify left side} \\[1 em]12x+1 &= 3&& \text{ move 1 to the right } \\[1 em]12x &= 3-1&& \\[1 em]12x &= 2&& \text{ divide both sides by $ 12 $ } \\[1 em]x &= \frac{2}{12}&& \\[1 em]x &= \frac{1}{6}&& \\[1 em] \end{aligned} $$

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