Answer
$[Mn(H_{2}O)_{4} Br_{2}]ClO_{4}$
Work Step by Step
The formula is written according to the rules of writing the formula for complex compounds.
1. tetraaquadibromomanganese(III) is the cation whereas perchlorate is the anion. Cations are written first, then are anions.
2. tetraaquadibromo is the ligand whereas manganese(III) is a metal. Metal is written first then is the ligand.
3. tetraaquadibromo, tetraaqua means 4 molecules of water: $(H_{2}O)_{4}$ and dibromo means $Br_{2}$.
4. From point number 2 and 3, we have: $[Mn(H_{2}O)_{4} Br_{2}]$
5. Manganate(III) means Manganate has a +3 charge. Perchlorate has a -1 charge. $ClO_{4}^{-1}$.
6. In order to check if the charge on the cation and anion is balanced, we take out the charge on the cation:
Since water has no charge: $ 4\times 0=0$
$+3+0+2\times(-1)$
$+3-2=+1$
Hence the charges are balanced, Therefore the formula of the complex is:
$[Mn(H_{2}O)_{4} Br_{2}]ClO_{4}$
