For this problem, we want to first write out our reactants and our products. Butane and O2 (O2 will always be a reactant for a combustion reaction) are our reactants while our products are carbon monoxide and water
C4H10 + O2 ----> CO2 + H2O
Now that we have our equation, we need to balance it. To do this I like to write out each element and how many we have on each side of the equation.
C4H10 + O2 ----> CO2 + H2O
C: 4 | C: 1
H: 10 | H: 2
O: 2 | O: 3
Now, when balancing combustion reactions particularly, you should balance oxygen last. The reason for this is that we see it in two molecules on the right side of the equations so it is hard to determine which one should be increased to balance the left side. Thus, I start with carbon, then hydrogen, and lastly oxygen.
First carbon (it changes also the number of oxygens here don't forget- now 8 from CO2 vs the 2 before):
C4H10 + O2 ----> 4 CO2 + H2O
C: 4 | C: 4
H: 10 | H: 2
O: 2 | O: 9
Now hydrogen:
C4H10 + O2 ----> 4 CO2 + 5 H2O
C: 4 | C: 4
H: 10 | H: 10
O: 2 | O: 13
Lastly oxygen:
C4H10 + 6.5 O2 ----> 4 CO2 + 5 H2O
C: 4 | C: 4
H: 10 | H: 10
O: 13 | O: 13
HOWEVER, we cannot have decimals or fractions for the coefficient (cannot have 6.5). To get rid of this .5 we would need to double each molecule's coefficients.
Removing the decimal coefficient :
2 C4H10 + 13 O2 ----> 8 CO2 + 10 H2O
C: 8 | C: 8
H: 20 | H: 20
O: 26 | O: 26
Therefore the final answer should be (don't forget phases!!!)
2 C4H10 (g) + 13 O2 (g) ----> 8 CO2 (g) + 10 H2O (g)
I hope this was easy to follow and allows to approach balancing equation questions