How did you get 1.63 X 10^19 particles? You have all the working out correct... but not the answer.

First part is correct, 0.125g * 0.0417 = 0.0052125 moles of hydrogen

The next part, you have the method correct, but not the answer.

The Avogadro constant is 6.022×(10^23)

0.0052125 moles * [6.022×(10^23)] = ...

I'm sure you can type that into the calculator yourself?

And you shouldn't get 1.63 X 10^19.