The horizontal asymptote is determined by the degree in the numerator and denominator, and (in case you forgot) the degree of a polynomial is the highest exponent of that polynomial.
In this problem, the degree of the numerator is 3 (from 8x^3) and in degree of the denominator is 2 (from 35x^2). Since the degree in the numerator is greater than the degree of the denominator, we don't get a horizontal asymptote. [NOTE: the only time we get a horizontal asymptote is when the degrees are the same or if the degree of the denominator is greater.]
In this case, all we get is a slant asymptote. To find out what that asymptote is, use polynomial division. (If you have never heard of a "slant asymptote" or "polynomial division" then forget I mentioned this and just know there is no horizontal asymptote.)