Answer
The solution is $g=27$.
Work Step by Step
The given equation is
$\Rightarrow 6=\sqrt[3]{8g}$
Cube each side of the equation.
$\Rightarrow 6^3=(\sqrt[3]{8g})^3$
Simplify.
$\Rightarrow 216=8g$
Divide each side by $8$.
$\Rightarrow 27=g$
Check $g=27$.
$\Rightarrow 6=\sqrt[3]{8(27)}$
$\Rightarrow 6=\sqrt[3]{216}$
$\Rightarrow 6=\sqrt[3]{6^3}$
$\Rightarrow 6=6$
True.
Hence, the solution is $g=27$.
