Hi Gmat_mission.

Here, using the zero product rule we have that $$\left(6+\frac{2}{x}\right)\left(x-4\right)=0\ \ \ \ \Rightarrow\ \ 6+\frac{2}{x}=0\ \ \ \ \ \ or\ \ \ \ \ \ \ x-4=0$$ $$\Rightarrow\ \ \frac{2}{x}=-6\ \ \ \ \ \ or\ \ \ \ \ \ \ x=4$$ $$\Rightarrow\ x=-\frac{1}{3}\ \ \ \ \ \ or\ \ \ \ \ \ \ x=4$$ But on the other hand, we are told that \(x\) does not equal to \(4\), then we have that \(x=-\frac{1}{3}.\)

So, the correct answer is the option [spoiler]C) -1/3[/spoiler].

I hope it is clear. <i class="em em-sunglasses"></i>