Answer
$15.9847\ amu$
Work Step by Step
1. Let us call this new unit as $mol_a$. We know that this new unit is defined as the number of atoms in 12g of C. To convert some unit measured in moles to this new $mol_a$, we first need a conversion factor.
$12.011g/mol=12g/mol_a$ Therefore $1g/mol= 0.9991g/mol_a$
2. Now, when we have the conversion factor, we can convert any value from one unit to another:
$15.9994g/mol\times0.9991mol/mol_a= 15.9847g/mol_a$
The atomic mass of oxygen in this condition would be 15.9847 amu.