Answer
$x=\dfrac{1}{2}$
Work Step by Step
Raising both sides to the third power results to
\begin{array}{l}\require{cancel}
2(1-x)^{1/3}=4^{1/3}
\\\\
\left( 2(1-x)^{1/3} \right)^3=\left( 4^{1/3} \right)^3
\\\\
8(1-x)=4
.\end{array}
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
8(1-x)=4
\\\\
8(1)+8(-x)=4
\\\\
8-8x=4
.\end{array}
Using the properties of equality to isolate the variable results to
\begin{array}{l}\require{cancel}
8-8x=4
\\\\
-8x=4-8
\\\\
-8x=-4
\\\\
x=\dfrac{-4}{-8}
\\\\
x=\dfrac{1}{2}
.\end{array}