How do you balance c2h2 + o2 -> co2 + h2o? ? is it c2h2 + 5/2 o2 -> 2co2 + h2o or 2c2h2 + 5o2 -> 4co2 + 2h2o ?

The balance equation is

C2H2 + (5/2)O2 -> 2CO2 + H2O (which is the first option)

Removing the fraction yields

2C2H2 + 5O2 -> 4CO2 + 2H2O (which is the second option)

However the second option is preferred since there is no fraction.

Having whole number coefficients is sometimes important especially when the coefficient is interpreted as number of molecules.