Calculate the number of atoms of oxygen present in 1.3 mol of sulfuric acid
The key about the unit mole is that it does not reference which type of entity is specified. Using the mole only makes sense if you define what you are using the mole for. This could be:


protons
atoms
ions
molecules
formula units of an ionic or metallic solid
aggregates
apples
stars
…


The mole is basically just a large number that you can use instead of e.g. the number 1,000,000 or the number 0.5.

So in your question, $\pu{1.3 mol}$ of $\ce{H2SO4}$ means that you have $1.3 \times 6.022 \times 10^{23}$ molecules of $\ce{H2SO4}$, each of which contains one sulphur atom, two hydrogen atoms and four oxygen atoms. Thus, in one mole of $\ce{H2SO4}$ you can find:


$\pu{2mol}$ of hydrogen atoms
$\pu{1mol}$ of sulphur atoms
$\pu{50 mol}$ of protons
$\pu{50mol}$ of electrons
and $\pu{4mol}$ of oxygen atoms.


The correct solution is thus:

$$n(\ce{O}) = 4\times n(\ce{H2SO4}) = 4 \times 1.3 \times 6.022\times 10^{23} = 3.13 \times 10^{24}$$