Step 1: Understand the IUPAC naming convention.
The IUPAC name "Tetraaminedibromoplatinum (IV) bromide" indicates the following:
- "Tetraamine" refers to four ammonia molecules (\(NH_3\)) coordinated to the platinum ion.
- "Dibromo" indicates two bromine atoms as ligands.
- The platinum is in the +4 oxidation state, hence "platinum (IV)".
- The bromide (\(Br\)) ion is a counter ion.
Step 2: Writing the formula.
The formula for this complex is:
\[
\text{[PtBr}_2(\text{NH}_3)_4\text{]} \text{Br}
\]
Thus, the correct answer is (A).