The easiest way to do this is to balance the carbon and hydrogen atoms, and then balance the oxygen atoms.
#"C"_10"H"_20"O"_2+"O"_2 rarr "CO"_2 + "H"_2"O"#
We have #10# #"C"# atoms on the LHS, so we must have the same on the right hand side:
#"C"_10"H"_20"O"_2+"O"_2 rarr color(red)(10)"CO"_2 + "H"_2"O"#
We have #20# #"H"# atoms on the LHS, so that will give us #10# #"H"_2"O"# molecules:
#"C"_10"H"_20"O"_2+"O"_2 rarr color(red)(10)"CO"_2 + color(blue)(10)"H"_2"O"#
On the RHS we have #30# #"O"# atoms, and on the left, #2#. This means we'll need #14# #"O"_2# atoms to balance the equation:
#"C"_10"H"_20"O"_2+color(green)(14)"O"_2 rarr color(red)(10)"CO"_2 + color(blue)(10)"H"_2"O"#
