How many moles of carbon atoms are present in a piece f diamond?

Diamond is an allotrope of carbon; that just means it is a different crystalline structure, but pure diamond contains only carbon atoms. (unrelated, but interesting - colored diamonds come from impurities like boron and nitrogen in the crystal structure!) The molar mass of carbon is 12.01 g/mol. You can find the molar mass by looking at the periodic table. If you look under number 6, Carbon, you should see the atomic weight right under it: 12.01. The molar mass is this same number, in grams. That means that one mole, or 6.022E23 carbon atoms, weigh 12.01 grams. 
But you don't have one mole. You only have 2 grams. 
So how many moles do you have? 2 grams out of 12 grams. 2/12 = 1/6 or 0.167. You have 1/6th of a mole. One mole is 6.022E23 atoms, but you only have 1/6th of that. I hope that thinking about it stepwise like this makes sense to you. It works the same for other atoms and molecules too. In a molecule, you would just add up the molar mass of all the component atoms. I hope this helps.