One mole of methane specifies #N_A#, #"Avogadro's number"# of methane molecules, i.e. #6.022xx10^23# individual #CH_4# molecules. And thus it contains #4xx6.022xx10^23# #"hydrogen atoms"#.
I would have used precisely the same procedure if I were asked the number of #"hydrogen atoms"# in #"4 dozen methane molecules"#; i.e. there are #4xx12=48#, #"four dozen"#, #"hydrogen atoms....."# The mole is simply a collective number like a #"dozen"# or a #"gross"#.....admittedly, it is a much larger quantity.
The #"mole"#, however, has a special property: #N_A# #""^12C# atoms have a mass of #12.0*g# precisely, and thus we use it as a means to equate the number of atoms, which we can estimate but not individually count, with a given mass of stuff.
