#### Answer

$18\sqrt[3]{2m}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
6\sqrt[3]{128m}-3\sqrt[3]{16m}
,$ simplify first each term by expressing the radicand as a factor that is a perfect power of the index. Then, extract the root. Finally, combine the like radicals.
$\bf{\text{Solution Details:}}$
Expressing the radicand as an expression that contains a factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
6\sqrt[3]{64\cdot2m}-3\sqrt[3]{8\cdot2m}
\\\\=
6\sqrt[3]{(4)^3\cdot2m}-3\sqrt[3]{(2)^3\cdot2m}
.\end{array}
Extracting the roots of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
6(4)\sqrt[3]{2m}-3(2)\sqrt[3]{2m}
\\\\=
24\sqrt[3]{2m}-6\sqrt[3]{2m}
.\end{array}
By combining like radicals, the expression above is equivalent to
\begin{array}{l}\require{cancel}
(24-6)\sqrt[3]{2m}
\\\\=
18\sqrt[3]{2m}
.\end{array}