[tex]4NH_3 + 5O_2 \rightarrow 4NO + 6H_2O[/tex]
We're given:
The mole ratio between NH3 and O2 is 4:5, meaning...
[tex]\dfrac{n(NH_3)}{4}=\dfrac{n(O_2)}{5}[/tex]
Plug in the given moles of NH3 and solve for moles of O2:
[tex]\dfrac{16}{4}=\dfrac{n(O_2)}{5}[/tex]
[tex]n(O_2)=20[/tex]
20 moles of O2 are needed to completely react with 16 moles of NH3.