How do I get this answer?
A lazy way is to use l'Hopital's Rule twice.
A not so lazy way is to substitute the power series for cos(2x) and cos(3x), simplify and then take the limit.
Another not so lazy way is to use the well known limit $\displaystyle \lim_{t \to 0} \frac{\cos (t) - 1}{t^2} = 1$.