Moles chemistry question

Admittedly even at A-level I'm still a little shaky on the definition of a mole. I understand that a mole of a substance contains 6.02 x 10^23 grams, but with that knowledge I can't seem to get the right answer to this question:

What is the number of atoms in 2.8 grams of ethene?
Data given: Molar mass of C2H4 is 28g mol-1, Avogadro constant is 6.0 x 10^23

My working is:

28 g of ethene = 6.0 x 10^23 atoms
therefore 2.8g of ethene = 6.0 x10^22 atoms

The correct answer is 3.6 x 10^23 grams. I know that there are 6 atoms in an ethene molecule but how do I use that to arrive at the correct answer? Does one mole of ethene not contain 6.0 x10^23 atoms?

Thanks

One mole of ethene contains 6.0x10^23 molecules, not atoms. So 2.8g is 0.1 moles or 6.0x10^22 molecules. Then multiply that by 6 because there are 6 atoms in an ethene molecule.