First, write a balanced chemical equation of the reaction:

 C\(_2\)H\(_5\)OH  +  3 O\(_2\) → 2 CO\(_2\) + 3H\(_2\)O

  3moles : 2 moles

 Using  n = \(\frac{mass}{Molar mass}\), \(\frac{6}{32}\)  :  x mole

  0.1875 mole :  x mole

By simple proportion, X = \(\frac{0.1875  X 2}{3}\)

 X = 0.125 mole