#### Answer

$m=6$

#### Work Step by Step

Using the properties of equality, the solution to the given equation, $
2(3+4m)-6=48
$, is
\begin{array}{l}
6+8m-6=48
\\\\
8m=48
\\\\
m=\dfrac{48}{8}
\\\\
m=6
.\end{array}
CHECKING:
\begin{array}{l}
2(3+4\cdot6)-6=48
\\\\
2(3+24)-6=48
\\\\
2(27)-6=48
\\\\
54-6=48
\\\\
48=48
\text{ (TRUE)}
.\end{array}
Hence, the solution is $
m=6
$.