Question

When 2.05 moles of CH4 are mixed with 5.03 moles of O2 in the reaction below, the limiting reactant is
CH4 + 2O2 -> CO2 + 2H2O

Answer 1

CH4 is the limiting reactant

Answer 2

I agree that CH4 is the LR but here is how you prove it.
Convert 2.05 mols CH4 to mols needed for O2.
2.05 mols CH4 x (2 mols O2/1 mol CH4) = 4.10 mols O2 needed. Do you have that much? Yes. So CH4 is the limiting reagent.