Each carbon atom will react with 4 hydrogen atoms to form methane (

) Since there are 2 hydrogen atoms in a hydrogen molecule (

) then each carbon atom will react with 2 hydrogen molecules. Since there are 22 hydrogen molecules half as many methane molecules will be formed, so 11. Then we can subtract 11 from 34 to find the number of carbon atoms left over.
So in summary, 11 methane molecules will be formed and there will be 23 carbon atoms left over.
There are three ways that scientists have proved that these sub-atomic particles exist. They are direct observation, indirect observation or inferred presence and predictions from theory or conjecture. Scientists in the 1800's were able to infer a lot about the sub-atomic world from chemistry.