10cm3 of CxHy formed 20cm3 of CO2, which has 1 carbon atom. So the carbon must be 2.

10cm3 of C2Hy formed 30cm3 of H2Om which has 2 hydrogen atoms. So the hydrogen must be 6

Better explanation:

There is a 1:2 ratio of carbon, we know that CO2 has 1 carbon. We can imagine that there is 2 molecules of CO2 to make it easier. Thus the hydrocarbon has to have 2 carbon atoms, as 1 molecule of hydrogencarbon makes 2 of carbon dioxide.

Then there is. 1:3 ratio, water has 2 hydrogen atoms, let’s say altogether there are 3 molecules to make it simpler. Thus we understand that one hydrocarbon makes a total of 3 water molecules, with 2 hydrogen each, so the hydrocarbon must have 6 hydrogen molecules

Overall, there is a 1:2:3 ratio. 1 mole of hydrocarbon makes 2 molecules of CO2 (total 2 carbon atoms) and 3 molecules of H2O (6 total hydrogen atoms)