This part isn't wrong but it is unnecessary.
0.4 x 6x10^23 = 2.4x10^23 molecules of CH4
(as there are 5 atoms in 1 molecule we multiply by 5)
2.4x10^23 x 5 = 1.2x10^24 atoms
(4 fifths of atoms are hydrogens so...)
1.2x10^24 / 5 x 4 = 9.6x10^23 atoms of hydrogens
The problem asks for moles of H (not atoms of H) and you already have an expression for moles of H in terms of moles of methane. So rather than (methane mass --> methane moles --> methane molecules --> H atoms --> H moles) you can do (methane mass --> methane moles --> H moles).
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1 mol methane = 4 moles Hydrogen