I assume the equation described is:
( x + 6 ) / ( x^2 - 64 )
You can compare the degree of the numerator and denominator in a function that takes the form of this type of rational equation.
Here are the three rules
#1 (Correct Answer): When the degree of the numerator is smaller then the denominator the horizontal asymptote is y = 0
#2 If the degree of the numerator and denominator is the same, then you take the leading coefficient of the numerator (n) and denominator (d) to create the answer y = n / d in this equations case it would be 1 / 1 since variables technically have an invisible 1 in front of them since anything multiplied by 1 is its self, 1x = x
#3 When the degree of the numerator is greater then the degree of the denominator then this means that it does not have a horizontal asymptote.
Again the final answer is that the horizontal asymptote is y = 0