Answer
$4NH_{3}(g)+5O_{2}(g)\ -->\ 4NO(g)+6H_{2}O(g)$
Work Step by Step
Write out the equation without coefficients. Add a coefficient of 4 to ammonia and nitrogen monoxide. Now add a 6 to the water to balance the hydrogen from the ammonia. Add a 5 to the oxygen to balance out the 4 oxygen from oxygen monoxide and the 6 from water.