Determining an empirical formula from combustion data

https://www.khanacademy.org/science/ap-chemistry/stoichiometry-and-molecular-composition-ap/molecular-composition-ap/v/worked-example-determining-empirical-formula-from-combustion-data?modal=1

In a following video it is said that 3.47 grams of H2O is 0.193 moles.
Then it is multiplied by 2, so that to know H, which makes me confused.

It is illogical, since we have found moles for H2O molecule, dividing grams of H20 in a reaction (3.47) by atomic weight of H2O (18). The result is 0,193 which is how many of H2O atoms is in 3.47 grams given in the reaction. Why then in order to know how much of H we multiply 0.193 by 2, if that will mean only knowing how much moles does 2 (H20) have?
Instead, why we don't work within the number of 0.193 which includes both Hydrogen and Oxygen in the ratio of 2/1?

And why do moles of C in a product CO2 equal 0.128, which is an amount of moles of the whole of 5.65 gr of CO2? So,  in order to know amount of moles of C in CO2 we should also work within 0.128

And only then with those numbers we can get the ratio of C in CO2 to H in H2O, which will determine how the empirical formula will look like.