What is the correct IUPAC name of K_3[Fe(CN)_6] ?

The given coordination compound is $\text{K}_3[\text{Fe(CN)}_6]$.

The cation is potassium and the complex anion is $[\text{Fe(CN)}_6]^{3-}$.

Let the oxidation state of iron (Fe) be $x$.

The charge on each cyanide (CN) ligand is $-1$.

Equating the sum of oxidation states to the charge on the complex ion:

$x + 6(-1) = -3$

$x - 6 = -3$

$x = +3$

The complex anion contains six cyanide ligands, which are named as 'hexacyano'.

Since the complex is an anion, the suffix '-ate' is added to the Latin name of iron, making it 'ferrate'.

The oxidation state is written in Roman numerals in parentheses as (III).

Combining these parts, the IUPAC name is Potassium hexacyanoferrate(III).

Answer: Potassium hexacyanoferrate(III)