#### Answer

$m\gt\dfrac{7}{3}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
5[3m-(m+4)]\gt-2(m-4)
,$ use the Distributive Property and the properties of inequality to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the inequality above is equivalent to
\begin{array}{l}\require{cancel}
5[3m-(m+4)]\gt-2(m-4)
\\\\
5[3m-1(m)-1(4)]\gt-2(m)-2(-4)
\\\\
5[3m-m-4]\gt-2m+8
\\\\
5[3m]+5[-m]+5[-4]\gt-2m+8
\\\\
15m-5m-20\gt-2m+8
.\end{array}
Using the properties of inequality to isolate the variable, then
\begin{array}{l}\require{cancel}
15m-5m-20\gt-2m+8
\\\\
15m-5m+2m\gt8+20
\\\\
12m\gt28
\\\\
m\gt\dfrac{28}{12}
\\\\
m\gt\dfrac{7}{3}
.\end{array}