The Equation given in statement is as follow,
2 C₂H₂ + O₂ → 4 CO₂ + H₂O
According to equation,
Carbon atoms on reactant side are 4 in number, and that on product side are also 4 in number. SO, carbon atoms are balanced.
Hydrogen atoms on reactant side are 4, and on product side are 2. Means Hydrogen atoms are not balance. So, to balance them multiply H₂O with 2. So,
2 C₂H₂ + O₂ → 4 CO₂ + 2 H₂O
Now, calculate number of Oxygen atoms on both sides. There are 2 Oxygen atoms on reactant side and 10 Oxygen atoms on product side. So, to balance them multiply O₂ on reactant side with 5. So,
2 C₂H₂ + 5 O₂ → 4 CO₂ + 2 H₂O
Above Equation is balanced.