Step by step instructions on how to balance
c2h2 + o2 = co2 + h2o

First, notice the H2O on the products. That will make an odd # of Oxygen on the right side, so you'll give H2O a coefficient of 2 to make it even. (No matter what coefficient you use on the left, the number of Oxygen will always be even) 

2. Then, give C2H2 a coefficient of 2 to make 4 hydrogen, because the 2H2O now makes 4 hydrogen on the right side. 

3. Thus, put a 4 in front of CO2 to make it even with the left side. 

4. Finally, count up the O on the right side (10). 

5. Put a 5 on the left side in front of O2, to make it add up to 10. 

6. make sure each side as the same number of atoms for each element. 4C, 4H, 10O