How many moles is 1.81 x 10^24 atoms of carbon?

Well a number you have to know is 6.02 x 10^23. That is how many atoms there are in a mole.

So if you have 1.81 x 10^24 atoms,
you divide that by 6.02 x 10^24 moles to get 3 moles

Using factor/label method:
1.81 x 10^24 atoms * 1 mol
                                      = 3 moles
                                   6.23 x 10^23 atoms
(As you can see, the unit "atoms" cancels out from the top and bottom.)