from the balanced equation 4NH3 +7O2 - 4NO2 + 6H2O

Question

How many molecules of water are produced when 2.25 moles of ammonia are completely reacted?

The equation tells us that 4 mol NH3 will produce 6 mols water. That means 2 mols NH3 will produce 3 mols water. How did we do that?
2 mols NH3 x (6 mols H2O/4 mols NH3) = 3 mols H2O. Right? So that factor is what you use.
2.25 mols NH3 x (6 mols H2O/4 mols NH3) = ?? mols H2O.
We know there are 6.02 x 10^23 molecules in one mol. So how many molecules will be in ?? mol H2O.

2.25 mols NH3 x (6 mols H2O/4 mols NH3) = ?? mols H2O
3.4mols
3.4 x 6.02 x 10^23=2.05?

2.25 mols NH3 x (6 mols H2O/4 mols NH3) = ?? mols H2O
3.4mols My calculator gives 3.375 mols. You are allowed 3 places (since there are 3 in the original 2.25 number; therefore, rounding to 3.4 is too harsh. It should be rounded to 3.38 mols.

3.4 x 6.02 x 10^23=2.05?
What did you do with the 10^23?
3.38 x 6.02 x 10^23 = 2.03 x 10^24. Do that on your calculator. Check my arithmethic. I have trouble seeing the calculator buttons.

I got 2.03 x 10^25

No, 2.03 x 10^24 is correct. You may have punched in the wrong exponent.