To solve this problem, we need to understand the concepts of homoleptic and heteroleptic complexes.$\newline$• A homoleptic complex is one in which a metal ion is surrounded by only one type of ligand.$\newline$• A heteroleptic complex is one in which a metal ion is surrounded by more than one type of ligand.$\newline$Let's analyze the given statements:$\newline$Statement I:$[Co({NH}_3)_6]^{3+}$ is a homoleptic complex whereas [Co(NH$_3)_4Cl_2]^{+}$ is a heteroleptic complex.$\newline$• In$[Co(NH_3)_6]^{3+}$, the cobalt ion is surrounded by six ammonia (NH$_3)$ ligands, which are all the same.$\newline$• Therefore, [Co(NH$_3)_6]^{3+}$ is a homoleptic complex.$\newline$• In$[Co({NH}_3)_4Cl_2]^{+}$, the cobalt ion is surrounded by four ammonia (NH$_3)$ ligands and two chloride (Cl) ligands.$\newline$• Since there are two different types of ligands, [Co(NH$_3)_4Cl_2]^{+}$ is a heteroleptic complex.$\newline$Thus, Statement I is true.$\newline$Statement II: Complex [Co(NH$_3)_6]^{3+}$ has only one kind of ligand but [Co(NH$_3)_4Cl_2]^{+}$ has more than one kind of ligands.$\newline$• As analyzed above, [Co(NH$_3)_6]^{3+}$ has only ammonia ligands, so it has one kind of ligand.$\newline$• [Co(NH$_3)_4Cl_2]^{+}$ has both ammonia and chloride ligands, so it has more than one kind of ligand.$\newline$Thus, Statement II is true.$\newline$Therefore, both Statement I and Statement II are true.$\newline$This corresponds to Option 3.