I would approach it like this:
Since you need 3moles of H2 to react with 1mole N2, you know that H2 is limiting. Always use the limiting factor.
Since you have 1 mole of H2 and 3 moles of H2 are needed to yield 2 moles of NH3, do this:
1 mol H2 (have) * [ 2 moles NH3 / 3 moles H2 (needed)] = 2/3