How do you determine if and ion has a
noble-gasconfiguration?

Explanation:

Noble gas configuration is defined as the configuration which contains completely filled orbitals.

For example, oxygen atom when gain two electrons then it forms oxygen ion ().

Atomic number of oxygen atom is 8 and so, its number of electrons will also be 8. But when it gain two electrons then it has total 10 electrons. Hence, electronic configuration of is as follows.

Since, there are completely filled orbitals in an ions. Therefore, it means this ion has a  noble-gas configuration.

Thus, we can conclude that any specie which shows completely filled orbitals will have noble-gas configuration.

atomic number of carbon is 6

electronic configuration of carbon is 1s²2s²2p²

orbital diagram of c is as shown here in the image.