Avogadro’s number is “the number of things in a mole” in the same way that 12 is “the number or things in a dozen”.
*By definition*, 1 mole (Avogadro’s number) of carbon-12 atoms weighs 12 grams. That’s the connection, it’s just the definition. Oh, and for the “actual atomic mass”, we give that in “atomic mass units” which are grams per mole. So again it’s all kind of the same thing.
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