Thoroughly explain how to balance this chemical equation.

The coefficients are 8 17 1 8

remember that we have to have the same amount of atoms on each side of the equation.
start with C there is 1 on the left and 8 on the right so 8 has to be on the CO. now there is an 8 now on the water there is 1 originally and now we need 8. from water there is now a total of 16 hydrogen plus the 18 from octane for a total of 34. the left has an H2. 34/2 = 17. that is where the 17 comes from

Amethod of procedure that has characterized natural science since the 17th century, consisting in systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses.