How to find the order of a dihedral group made up of two elements of order $2$?

Question

I have a group $\langle x,y \rangle$ that is a dihedral group and nonabelian and $x,y$ both have order $2$. I have worked it out that the group $ \langle xy,y \rangle$ is equivalent to $\langle x,y \rangle$ such that the order of $xy$ is $n$. How would I go about finding $n$ such that the order of the group is $2n$?