Basic Knowledge

$\large 6^6=x^2 \cdot 6^3$

$\large \Rightarrow \dfrac{6^6}{6^3}=x^2$

$\large \Rightarrow 6^{(6-3)}=x^2$

$\large \Rightarrow 6^3=x^2$

$\large \Rightarrow x=\sqrt{6^3}$

$\large \Rightarrow x=\sqrt{6 \cdot6\cdot6}$

$\large \Rightarrow x=\sqrt{36\cdot6}$

$\large \Rightarrow x= \boxed{6\sqrt6}$

Go to wolframalpha.com and find a solution.

Here is link

Just kidding.

$6^6=x^2(6^3)$

$\dfrac{6^6}{6^3}=x^2$

$6^3=x^2$

$6(6^2)=x^2$

Extracting the square root of both sides, we get

$\pm 6\sqrt{6}=x$

Since it is asking for the positive value, our answer is

$\color{#D61F06}\boxed{x=6\sqrt{6}}$