Are both sides equal?

First of all, we should know that $\sqrt{a}\times\sqrt{b}$ is equal to $\sqrt{ab}$ and $a\sqrt{x}=\sqrt{a^{2}x}$ . So,

$\sqrt{x+ 8 - 4} \sqrt{x+6} = x \sqrt{2}\space \Rightarrow\space \sqrt{(x+4)(x+6)}=\sqrt{2x^2}$

Squaring both sides,

$(x+4)(x+6)=2x^2$

Solving the quadratic,we get: $x=-2\space or\space 12$

Since $x$ cannot be negative, $\Rightarrow\space x=12.$