0.151 moles
Ethanol is C2H6O, and the balanced reaction is
C2H6O + 3O2 ==> 2CO2 + 3H2O
Now calculate the molar mass of C2H6O. Start with the atomic weights.
Atomic weight carbon = 12.0107
Atomic weight hydrogen = 1.00794
Atomic weight oxygen = 15.999
Molar mass C2H6O = 2 * 12.0107 + 6 * 1.00794 + 15.999
= 46.06804 g/mol
Molar mass O2 = 2 * 15.999 = 31.998 g/mol
Determine how many moles of each reactant is available.
Moles C2H6O = 2.32 g / 46.06804 g/mol = 0.050360293 mol
Moles O2 = 10.6 g / 31.998 g/mol = 0.331270704 mol
Looking at the balanced equation and the number of moles of each reactant, it's obvious that the limiting reactant is C2H6O, and since each mole of C2H6O will produce 3 moles of H2O, then we just need to multiply the number of moles of C2H6O we have by 3, giving
0.050360293 mol * 3 = 0.151080879 moles
And of course, round to 3 significant figures, giving 0.151 moles.