Shouldn't the answer be E?
Because, if we plug in 6 then 6/(6-6)= 6/0= undefined.
The question doesn't ask for the value of X here, but for the possible results of the equation.
If 6/(x-6) = 0, then the numerator has to be 0 (just as you said, denominator can't be 0.) But since the numerator is 6, C can't be possible.
Hence the answer is C.