Answer
$x=18$.
Work Step by Step
$(\sqrt[3] {6})^{2x}=(\sqrt {6})^{x+6}$
This can be written as
$(6^{1/3})^{2x}=(6^{1/2})^{x+6}$
Using the property $(a^{m})^{n}=a^{mn}$, we get
$6^{\frac{2x}{3}}=6^{\frac{x+6}{2}}$
Equating the exponents, we have
$\frac{2x}{3}=\frac{x+6}{2}$
Multiply by $6$ on both sides to obtain
$4x=3x+18$
Subtracting $3x$ from both sides, we get
$x=18$
