So, in other words, one mole of atoms of carbon-12 is 6.02x10 23 carbon atoms. (Altogether, that many atoms weigh 12 grams.) ...

Rather than discussing such a large number of atoms, we can talk more conveniently through the mole unit. A mole of something contains 602,000,000,000,000,000,000,000 or 6.02 x 10²³ of that thing.