Step 1: Understanding heteroleptic complexes.
A heteroleptic complex contains two or more different types of ligands. In contrast, a homoleptic complex contains only one type of ligand.
Step 2: Analyzing the options.
(A) \([Pt(NH_3)_4Br_2]Br_2\): Incorrect. This is a heteroleptic complex because it contains two different ligands: ammonia (NH₃) and bromide (Br⁻).
(B) \([Co(NH_3)_6]Cl_3\): Correct — This is a homoleptic complex because it contains only one type of ligand, ammonia (NH₃).
(C) \([Co(en)_2Cl_2]^+\): Incorrect. This is a heteroleptic complex because it contains two different ligands: ethylenediamine (en) and chloride (Cl⁻).
(D) \([Co(en)_2Cl_2]Cl\): Incorrect. This is also a heteroleptic complex as it contains two different ligands: ethylenediamine (en) and chloride (Cl⁻).
Step 3: Conclusion.
The correct answer is (B) \([Co(NH_3)_6]Cl_3\), which is a homoleptic complex containing only one type of ligand.