Answer
{$\frac{3}{2}$}
Work Step by Step
For all positive numbers $a$, where $a\ne1$, and all positive numbers $x$, we know that $y=log_{a}x$ means the same as $x=a^{y}$.
Therefore, $log_{6}\sqrt 216=x$ means the same as $6^{x}=\sqrt 216$.
We know that $x=\frac{3}{2}$, because $6^{\frac{3}{2}}=(6^{3})^{\frac{1}{2}}=216^{\frac{1}{2}}=\sqrt 216$.