What is the IUPAC name for the complex ion [Co(NH3)6]3+ and what are its oxidation and coordination numbers?

The ligand is $NH_3$. In coordination chemistry, $NH_3$ is called ammine.

There are 6 $NH_3$ ligands. The prefix for six is hexa-. So, the ligand part is hexaammine.

The central metal atom is cobalt (Co).

Let the oxidation state of cobalt be $x$.
The charge of an ammonia ($NH_3$) ligand is 0 (it is a neutral molecule).
The overall charge of the complex ion is $+3$.
Set up the equation:

The oxidation state of cobalt is +3, which is written as (III) in Roman numerals.

For a cationic complex (positively charged), the name of the ligand(s) comes first, followed by the name of the central metal, and then its oxidation state in Roman numerals in parentheses. Since it's an ion, "ion" is added at the end.
Ligand name + Metal name(Oxidation state) + ion
hexaammine + cobalt + (III) + ion

The name of the complex ion is:

a) (ii) Determining the oxidation number and coordination number

Oxidation Number:
The oxidation number (or oxidation state) of the central metal ion represents the charge it would have if all ligands were removed along with their electron pairs.

The $NH_3$ ligand is neutral, so its charge is 0.
The overall charge of the complex ion $[Co(NH_3)_6]^{3+}$ is $+3$.

Let the oxidation number of Co be $x$.
The sum of the oxidation numbers of the central metal and all ligands must equal the overall charge of the complex ion.

The oxidation number of cobalt is +3.

Coordination Number:
The coordination number is the total number of donor atoms from the ligands that are directly bonded to the central metal ion.

The ligand is $NH_3$. Ammonia is a monodentate ligand, meaning it forms one coordinate bond to the central metal ion through its nitrogen atom.

There are 6 $NH_3$ ligands.
Since each $NH_3$ ligand is monodentate (denticity = 1), the coordination number is:

The coordination number of cobalt is 6.

Oxidation number: $\boxed{+3}$
Coordination number: $\boxed{6}$