# Hoeffding to bound Orlicz norm

I have been reading from Weak Convergence and Empirical Processes, and came across the following: Let $$a_1,\ldots,a_n$$ be constants and $$\epsilon_1,\ldots,\epsilon_n\sim$$Rademacher. Then

$$\mathbb{P}\left(\left|\sum_i\epsilon_i a_i\right|>x\right)\leq 2\exp\left(-\frac{x^2}{2||a||^2_2}\right)$$

Consequently, $$||\sum_i\epsilon_ia_i||_{\Psi_2}\leq\sqrt{6}||a||_2$$.

How does this follow (relation between Orlicz norm of Rademacher average and L2 norm of constants)? Thank you in advance for your time.