Answer
$(-\infty,2)\; or \; (2,+\infty)$.
Work Step by Step
The given functions are
$f(x)=\frac{8x}{x-2}$ and $g(x)=\frac{6}{2-x}$
$\Rightarrow f(x)+g(x)=\frac{8x}{x-2}+\frac{6}{2-x}$
Multiply and divide the second fraction:
$\Rightarrow f(x)+g(x)=\frac{8x}{x-2}+\frac{-6}{-(2-x)}$
$\Rightarrow f(x)+g(x)=\frac{8x}{x-2}-\frac{6}{x-2}$
Add both numerators because both denominators are equal.
$\Rightarrow f(x)+g(x)=\frac{8x-6}{(x-2)}$
In the denominator the value of $x$ must not be $-8$ and $4$.
Hence, the domain is $(-\infty,2)\; or \; (2,+\infty)$.
