Given that 4 nh3 + 5 o2 → 4 no + 6 h2o, when 4.50 mol of h2o are formed, the amount of no formed is 3.00 mol.

We need to examine the balancing coefficients of this equation.
4 NH3 + 5 O2 → 4 NO + 6 H2O

From the above equation, it is clear that the formation of 4 moles of NO is accompanied by the formation of 6 moles of H2O.
This means that the ratio between NO:H2O is 2:3

Based on this, if 4.5 moles of H2O are formed then number of NO moles formed (given the symbol n) will be calculated as:
n = 4.5 x (2/3) = 3 moles (cross multiplication)

It is called a neutralization reaction