When subtracting fractions, we need a common denominator. The least common multiple of $4$ and $6$ is $12$. So we'll rewrite each fraction with a denominator of $12$:
\[\begin{aligned} -\dfrac{3}{4}-\left(-\dfrac{1}{6}\right) &= -\dfrac{3\cdot 3}{4\cdot 3}-\left(-\dfrac{1\cdot 2}{6\cdot 2}\right) \quad\text{Multiply the top and bottom by 3 and 2}\\ &= -\dfrac{9}{12}+\dfrac{2}{12} \quad\text{Multiply}\\ &= \dfrac{-9+2}{12}\quad\text{Combine the fractions}\\ &= \dfrac{-7}{12} \end{aligned}\] The fraction $-\dfrac{3}{4}-\left(-\dfrac{1}{6}\right)$ reduces to $\boxed{-\dfrac{7}{12}}$.
Reduce to simplest form.
\[-\dfrac{3}{4}-\left(-\dfrac{1}{6}\right)=\]
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