#### Answer

$n\gt\dfrac{3}{2}$

#### Work Step by Step

Multiplying both sides by the $LCD=
12
$ and then using the properties of inequalities, the solution to the given inequality, $
\dfrac{2}{3}n-\dfrac{1}{2}n\gt\dfrac{1}{4}
,$ is
\begin{array}{l}\require{cancel}
4(2n)-6(1n)\gt3(1)
\\\\
8n-6n\gt3
\\\\
2n\gt3
\\\\
n\gt\dfrac{3}{2}
.\end{array}