The IUPAC name of K$$_3$$[Co(C$$_2$$O$$_4$$)$$_3$$] is:

We need the IUPAC name of K$$_3$$[Co(C$$_2$$O$_4$$)$$_3$$].

First, identify the cation as K$$^+$$ (potassium) and the anion as [Co(C$$_2$$O$$_4$$)$$_3$$]$$^{3-}$$.
To determine the oxidation state of cobalt, let it be $$x$$ and write the charge balance equation $$x + 3(-2) = -3$$, from which $$x = +3$$.

Next, focus on naming the complex anion. The ligand C$$_2$$O$$_4^{2-}$$ is called oxalato. Since there are three such ligands, the prefix could be tri for simple ligands or tris when the ligand name already contains a numerical prefix. Oxalato does not have a numerical prefix, making “tri” technically correct; however, because oxalate is a polydentate ligand, it is often written as tris with parentheses.

Then the metal in the anionic complex is named cobaltate(III).

Combining these parts gives the full name potassium trioxalatocobaltate(III), corresponding to Option 4 and matching the stored answer. The answer is Option 4: potassium trioxalatocobaltate(III).