Answer
$x=3$ or $x=11$
Work Step by Step
We are given:
$(14-2x)^{2/3}=4$
We raise both sides to the $3$rd power:
$[(14-2x)^{2/3}]^{3}=4^{3}$
$(14-2x)^{2}=64$
$(14-2x)(14-2x)=64$
And distribute:
$196-56x+4x^{2}=64$
$196-56x+4x^{2}-64=0$
$4x^{2}-56x+132=0$
And factor:
$4(x^{2}-14x+33)=0$
$4(x-3)(x-11)=0$
Equate each factor to zero, then solve each equation for $x$:
$4(x-3)=0$ or $(x-11)=0$
$(x-3)=0$ or $(x-11)=0$
$x=3$ or $x=11$