The correct IUPAC name of [PtBr2(PMe3)2] is:

🧠 Three Naming Decisions

IUPAC-name questions for neutral complexes test three things at once:

1. Alphabetical order of ligand names (ignore multiplying prefixes).
2. Multiplier choice — di/tri/tetra for simple ligands, bis/tris/tetrakis for complex/composite ligand names.
3. Oxidation state in Roman numerals.

🗺️ Apply to $[\mathrm{PtBr_2(PMe_3)_2}]$

Ligands & alphabetical order. "Bromo" (B) comes before "(trimethyl)phosphine" (P, alphabetised by 't' or 'p'? — by first letter of the ligand stem, which is 't' for trimethylphosphine). Either way, bromo first. ✓

Multipliers.

• 2 × bromo → "dibromo" (simple ligand → di-).
• 2 × trimethylphosphine → "bis(trimethylphosphine)" (composite name → bis- to avoid confusion with "ditrimethyl-").

Oxidation state. $x + 2(-1) + 2(0) = 0 \Rightarrow x = +2$. So Pt(II).

Combine: dibromobis(trimethylphosphine)platinum(II).

⚡ The "Bis vs Di" Decision Tree

Use bis/tris/tetrakis whenever:

• The ligand name itself contains a numerical prefix (di, tri, etc.) — e.g. ethylenediamine, trimethylphosphine.
• Or the ligand name has multiple words / is enclosed in brackets.

Use di/tri/tetra for simple, single-word ligands (bromo, chloro, ammine, aqua).

⚠️ The Oxidation-State Drop

Option (4) writes "bis[bromo(trimethylphosphine)]platinum(II)" — totally wrong syntax (you don't bracket two different ligands together). Always pair multipliers with one ligand at a time.

$\boxed{\text{Answer: (3) dibromobis(trimethylphosphine)platinum(II)}}$