CLT for fourth powers of normals

Let $\{X_{n}\}_{n\ge 1}$ be a sequence of independent and identically distributed $N(0,1)$ random variables. Then, $$\lim_{n\to\infty}P\left(\frac{\sum_{i=1}^{n}X_{i}^{4}-3n}{\sqrt{32n}}\le\sqrt{6}\right)$$ is equal to