Answer
$1C_2H_5OH(l) + 3O_2(g) --> 2CO_2(g) + 3H_2O(l)$
Work Step by Step
1. Write the unbalanced equation:
$C_2H_5OH(l) + O_2(g) --> CO_2(g) + H_2O(l)$
2. Balance the number of Carbon moles:
$1C_2H_5OH(l) + O_2(g) --> 2CO_2(g) + H_2O(l)$
3. Fix the number of Hydrogen moles:
$1C_2H_5OH(l) + O_2(g) --> 2CO_2(g) + 3H_2O(l)$
4. Finally, since we can count 7 Oxygen moles in the right side, and we already have one in $C_2H_5OH(l)$, we can put a 3 next to $O_2(g)$ and the equation will be totally balanced
$1C_2H_5OH(l) + 3O_2(g) --> 2CO_2(g) + 3H_2O(l)$