One mole of methane specifies NA, Avogadro's number of methane molecules, i.e. 6.022×1023 individual CH4 molecules. And thus it contains 4×6.022×1023 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 4×12=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: NA 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.
