1. Identify the ions present in the compound

   The compound is: $[Ni(NH_3)_4][NiCl_4]$

   It consists of two coordination entities:

   • $[Ni(NH_3)_4]$
   • $[NiCl_4]$

2. Find the charge and oxidation state of each complex

   (i) For $[Ni(NH_3)_4]$

   • $NH_3$ is a neutral ligand.
   • So if oxidation state of Ni is $x$, then charge on the complex is $x$.

   (ii) For $[NiCl_4]$

   • Each $Cl^-$ has charge $-1$.
   • Let oxidation state of Ni be $y$.
   • Charge on complex: $y + 4(-1) = y - 4$

   Since the overall compound is neutral, one complex must be cationic and the other anionic.

   The common oxidation state here is Ni$(II)$:

   • $[Ni(NH_3)_4]^{2+}$
   • $[NiCl_4]^{2-}$

   Check:

   • In $[Ni(NH_3)_4]^{2+}$, Ni is $+2$.
   • In $[NiCl_4]^{2-}$, Ni is also $+2$ because $x-4=-2 \Rightarrow x=+2$

3. Name the cation first

   In naming salts, the cation is named first, then the anion.

   • $[Ni(NH_3)_4]^{2+}$ : ligands are ammine, so name is tetraamminenickel(II)

4. Name the anion complex

   • $[NiCl_4]^{2-}$ has chloro ligands and is an anionic complex, so metal name ends in -ate.
   • Therefore its name is tetrachloronickelate(II)

5. Write the full IUPAC name

   $[Ni(NH_3)_4][NiCl_4]$ is named: tetraamminenickel(II) tetrachloronickelate(II)

6. Match with the given options

   • A: Wrong order and anion not written as nickelate
   • B: Anion should be nickelate, not nickel
   • C: Correct
   • D: Wrong oxidation state and wrong naming

Therefore, the correct option is C.