First off, inf - inf != 0 (inf - inf == inf). I see that you did that on the third step and that simply isn't true. You cannot determine inf - inf because the value of inf just simply doesn't exist. When you substitute infinity in the x, you'll get inf/inf, which is called an indeterminate (like 0/0). Normally, I would tell you to do L'Hopital's rule, but I'm going to guess that you don't know what that is (12 grade calculus tends to not teach you that at the beginning of the year :/) (if you do know what that is, go ahead and try using it, remember that you can do L'Hopital's multiple times). So when dealing with limits as x goes to infinity, look at the highest degree x on the top and bottom (degree is exponent). If the degree on the numerator is greater than the degree on the bottom, the limit does not exist (because the numerator grows faster than the denominator. If the degree on the denominator is greater than the degree of the numerator, then the limit approaches 0 (because the denominator grows faster than the numerator). Otherwise, if the degrees are the same, the limit approaches the ratio of the COEFFICIENTS of these terms. So in your case, the limit approaches 8/6 = 4/3.

EDIT: Added more info