Answer:
8 is the only one that will work
Explanation:
(f o g)(x)=f(g(x)).
So this means the x will first be plug into g.
So let's check your choices.
g(6)=1/(6-6)=1/0 so 6 is not in the domain of g which means it isn't in the domain of (f o g).
g(8)=1/(8-6)=1/2 so this is a number so 8 is in the domain of g,
Let's check if 1/2 is in the domain of f.
f(1/2)=sqrt(6*1/2)=sqrt(3) so this is a number so since 1/2 is in the domain of f then 8 is in the domain of (f o g).
g(4)=1/(4-6)=1/(-2)=-1/2 so 4 is in the domain of g,
f(-1/2)=sqrt(6*-1/2)=sqrt(-3) so this is a problem because you can't square root negative numbers so -1/2 isn't in the domain of f, and therefore 4 isn't in the domain of (f o g).
g(2)=1/(2-6)=1/-4=-1/4 so 2 is in the domain of g.
f(-1/4)=sqrt(6*-1/4)=sqrt(-3/2) so again this is a problem because we can't square root negative numbers so -1/4 isn't in the domain of f, and therefore 2 isn't in the domain of (f o g).