Order of Convergence- Iterative Methods

Question

I have a review question that asks us to find the order of this iterative method: $U^{n+3}=U^n+\frac{3}{8}h[f^{n+3}+3f^{n+2}+3f^{n+1}+f^n]$. I really do not understand how to do this, since we've talked about the method of $\frac{|x_{n+1}-x^*|}{|x_n-x^*|^p}=L$, where p is the order of convergence, but I do not understand how to do this with this method. Could someone explain how this applies to our method? I don't need an answer, just an explanation on how to apply the concept!