What is the mass of hydrogen in one mole of aluminum hydroxide?

The first thing to do here is figure out the chemical formula for aluminium hydroxide.

Aluminium is located in group `13` of the periodic table, and forms `3+` cations, `"Al"^(3+)`. The hydroxide anion, `"OH"^(-)`, carries a `1-` charge, which means that a formula unit of aluminium hydroxide will look like this

`["Al"^(3+)] + color(blue)(3)["OH"^(-)] -> "Al"("OH")_color(blue)(3)`

Now, you can figure out the mass of hydrogen present in `1` mole of aluminium hydroxide by first determining how many moles if hydrogen you get in `1` mole of aluminium hydroxide.

Since `1` mole of aluminium hydroxide contains `color(blue)(3)` moles of hydroxide anions, which in turn contain `1` mole of hydrogen each, you can say that you will have

`"1 mole Al"("OH")_ color(blue)(3) -> color(blue)(3)color(white)(a)"moles OH"^(-) -> color(blue)(3)color(white)(a)"moles H"`

The problem tells you that the molar mass of hydrogen is equal to `"1.01 g mol"^(-1)`. This means that `1` mole of hydrogen has a mass of `"1.01 g"`.

You can thus say that one mole of aluminium hydroxide contains

`color(blue)(3)color(red)(cancel(color(black)("moles H"))) * "1.01 g"/(1color(red)(cancel(color(black)("mole H")))) = color(green)(|bar(ul(color(white)(a/a)color(black)("3.03 g H")color(white)(a/a)|)))`

I'll leave the answer rounded to three sig figs.