$$x-\frac{2}{3} = x+\frac{1}{4}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x-\frac{2}{3} &= x+\frac{1}{4}&& \text{multiply ALL terms by } \color{blue}{ 12 }. \\[1 em]12x-12\cdot\frac{2}{3} &= 12x+12\cdot\frac{1}{4}&& \text{cancel out the denominators} \\[1 em]12x-8 &= 12x+3&& \text{move the $ \color{blue}{ 12x } $ to the left side and $ \color{blue}{ -8 }$ to the right} \\[1 em]12x-12x &= 3+8&& \text{simplify left and right hand side} \\[1 em]12x-12x &= 11&& \\[1 em]0 &= 11&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = 11 } $ is FALSE, we conclude that the equation has no solution.
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