[Savager]

In the complex ion K₄[Ni(NCS)₆].4H₂O, the K+ ions are just there to neutralise the charge, as all solids complexes have to have an overall neutral charge and they attach to four of the NCS anions. Am I right?

But I don't understand what the actual role of the water molecules are. I know they're incorporated in the crystal structure, but where and why? Do they stabilise the structure?

[Mitch]

There just ligands. Look up ligand field theory in your textbook, your question is too broad.

[AWK]

The detailed structure (X-ray structure of this compound is not known).
Nickel thiocyanate is anhydrous.
The first possibility (my guess) is a mixed salt hydrate: nickel thiocyanate.potassium thiocyanate.water. This is based on low stability constants for nickel thiocyanate complexes. Up to K3 are only listed.
The next possibility K4[Ni(SCN)6] hydrate or its structural isomers that contain some water as ligand and thiocyanate up to 6 (or 4) ligands, the rest as unbounded anions and molecules.