I know that the order type of an ordering is the unique ordinal that it is order-isomorphic to. And I know that a lexicographic ordering on $\mathbb{N}$ x $\mathbb{N}$ is a well-order, so there should be a unique ordinal it's isomorphic to. But other than initial definitions, I can't wrap my head around where to even begin for this problem.
Any help would be appreciated! Thank you.