What you require is a value of a such that the numerator has a factor of so your limit exists. so you numerator must factor in the form of for some real number "b". take out a factor of 6 to make thing easier.
by comparing coefficients you can solve the equation for a and b, the given value of a is correct and for checking purposed only b is
so the limit is reduced to
Did you follow that all okay? Let me know if you want something further explained