One mole of atoms equals #6.022xx10^23# atoms.
The formula for methane, #"CH"_4"# indicates that one mole of the compound contains four moles of hydrogen atoms.
In order to determine how many hydrogen atoms there are in the given moles of methane, multiply the given moles by the mole ratio between #"CH"_4"# and #"H"# to get moles of #"H"#. Then multiply the moles #"H"# by #"6.022xx10^23# atoms/mol.
#4.2color(red)cancel(color(black)("mol CH"_4))xx(4"mol H")/(1color(red)cancel(color(black)("mol CH"_4)))="16.8 mol H"#
#16.8color(red)cancel(color(black)("mol H"))xx(6.022xx10^23"atoms H")/(1color(red)cancel(color(black)("mol H")))=1.0xx10^25" atoms H"#
(rounded to two sig figs due to #4.2# mol #"CH"_4"#)
