#### Answer

$n=-\dfrac{1}{3}$

#### Work Step by Step

Using the properties of equality and combining like terms, the value of the variable that satisfies the given equation, $
5n-4-n=-3n-6+n
,$ is
\begin{array}{l}\require{cancel}
5n-n+3n-n=-6+4
\\\\
6n=-2
\\\\
n=\dfrac{-2}{6}
\\\\
n=-\dfrac{\cancel{2}}{\cancel{2}\cdot3}
\\\\
n=-\dfrac{1}{3}
.\end{array}