When you study the Domain of a quatient of two polynomial functions, have in mind that you need to worry about the zeros in the function that goes in the DENOMINATOR.
In your case, the only zero you fear is that coming from the function:
g(x) = x - 8
and this function has a zero at the point x = 8
Then the quotient f/g is NOT defined at x=8 (meaning that x = 8 is NOT in the Domain of the quotient f/g.
Then the only correct answer is: The second one that states that the Domain is All Real numbers except for x = 8 because the denominator is ZERO.