Start with a balanced equation which you already have.
4NH3 + 5O2 = 4NO + 6H2O
Now ask yourself, "what do I want to find". You want to know how many moles of NO are produced.
What are you given? You are given that you start with 6.96 g NH3 and excess O2.
Now you need the correct conversion factor. The conversion factor is a fraction with the numerator containing the quantity you are trying to find, and the denominator containing what you are given.
4 moles NO / 4 x mol mass of NH3 Note that the numerator is in moles of NO which is the coefficient of NO in the balanced equation. The denominator includes the coefficient for NH3 x mol. mass of NH3. It should be this way whenever a substance is given in grams. Putting numbers in the factor gives you
4 moles NO / 4 x 17.031 g /mole = 0.0587 moles NO per gram of NH3. Now multiply the factor result by the number of grams NH3 you were given.
0.0587 moles NO / g NH3 x 6.96 g NH3 = 0.409 g NO produced.
This is probably not how it is taught, but I find it more straightforward.