Step 1: Understanding the Concept
A homoleptic complex has the metal bound to only one kind of ligand. A heteroleptic complex has more than one kind.
Step 2: Check each option
Bis(ethylenediamine)dithiocyanatoplatinum(IV) has en and SCN, so it is heteroleptic.
Triamminetrinitrocobalt(III) has \(\text{NH}_3\) and \(\text{NO}_2\), and triamminetrithiocyanatorhodium(III) has \(\text{NH}_3\) and SCN, so both are heteroleptic.
Step 3: Conclusion
Tetraamminecopper(II), \([\text{Cu}(\text{NH}_3)_4]^{2+}\), has only ammine ligands, so it is homoleptic.
Final Answer:
The homoleptic complex is the tetraamminecopper(II) ion.
\[ \boxed{\text{(B) }\text{Tetraamminecopper(II) ion}} \]