The IUPAC name of the complex \([Pt(NH_3)_3Br(NO_2)Cl]Cl\) is

Triamminebromidochloridonitroplatinum (IV) chloride

The IUPAC name of the complex \([Pt(NH_3)_3Br(NO_2)Cl]Cl\) step by step:

1. Start with the central metal atom: The central metal atom is platinum (Pt). This is the metal ion that forms the coordination complex.

2. Identify the ligands: The ligands are the molecules or ions that surround the central metal ion. In this complex, we have four ligands:
   - Ammonia (NH₃) - acting as a tridentate ligand, which means it can donate three pairs of electrons to the metal ion.
   - Bromide ion (Br^-) - acting as a monodentate ligand, donating one pair of electrons.
   - Nitro group (NO₂^-) - also acting as a monodentate ligand, donating one pair of electrons.
   - Chloride ion (Cl^-) - acting as a monodentate ligand, donating one pair of electrons.

3. Determine the coordination number: The coordination number is the number of ligands coordinated to the central metal ion. In this complex, the coordination number is 6 because there are six ligands (three ammonia molecules, one bromide ion, one nitro group, and one chloride ion) coordinated to the platinum ion.

4. Alphabetical order of ligands: When writing the IUPAC name, the ligands are listed in alphabetical order. In this case, "bromide" comes before "chloride," so bromide is listed first.

5. Prefixes and suffixes: Use appropriate prefixes and suffixes to indicate the number of each ligand in the complex.
   - Triammine: "Tri-" is the prefix indicating there are three ammonia molecules (NH3).
   - Bromido: "Bromo-" is the prefix indicating one bromide ion (Br^-).
   - Chlorido: "Chloro-" is the prefix indicating one chloride ion (Cl^-).
   - Nitro: "Nitrato-" is the prefix indicating one nitro group (NO₂^-).

6. Oxidation state of the central metal ion: The oxidation state of the platinum ion is +4. This is indicated by the Roman numeral in parentheses, which follows the name of the central metal ion.
   - Platinum (IV): The Roman numeral "IV" indicates the +4 oxidation state of platinum.

Putting it all together, we get the complete IUPAC name of the complex: (c ) Triamminebromidochloridonitroplatinum(IV) chloride