How many of the following complexes are expected to have `d^(2)sp^(3)` hybridisation ?
`[Mn(CN)_(6)]^(3-)," "[MnCl_(6)]^(3-),`
`[Fe(CN)_(6)]^(3-),[FeF_(6)]^(3-)," "[CoF_(6)]^(3-),`
`[Co(C_(2)O_(4))_(3)]^(3-)," "[MnBr_(4)]^(2-)`

Explanation

To determine how many of the given complexes exhibit `d^(2)sp^(3)` hybridization, we need to analyze each complex based on the oxidation state of the central metal ion and the nature of the ligands involved.

### Step-by-Step Solution:

1. **Identify the oxidation state of the central metal ion**:
- For each complex, we need to find out the oxidation state of the metal ion.

2. **Determine the electron configuration**:
- Based on the oxidation state, we will determine the electron configuration of the metal ion.

3. **Analyze the ligands**:
- Identify whether the ligands are strong field or weak field ligands. Strong field ligands cause pairing of electrons, while weak field ligands do not.

4. **Determine the hybridization**:
- Based on the number of paired and unpaired electrons, we can determine if the hybridization is `d^(2)sp^(3)`.

Now, let's analyze each complex:

1. **[Mn(CN)₆]³⁻**:
- Oxidation state of Mn = +3 (since CN is a -1 ligand, 6 * -1 = -6, thus Mn must be +3).
- Electron configuration of Mn (Z=25) in +3 state: [Ar] 3d⁴.
- CN is a strong field ligand, leading to pairing of electrons: 3d².
- Hybridization: `d²sp³`.

2. **[MnCl₆]³⁻**:
- Oxidation state of Mn = +3.
- Electron configuration of Mn in +3 state: [Ar] 3d⁴.
- Cl is a weak field ligand, so no pairing occurs: 3d⁴.
- Hybridization: `sp³d²` (not `d²sp³`).

3. **[Fe(CN)₆]³⁻**:
- Oxidation state of Fe = +3.
- Electron configuration of Fe in +3 state: [Ar] 3d⁵.
- CN is a strong field ligand, leading to pairing of electrons: 3d⁵.
- Hybridization: `d²sp³`.

4. **[FeF₆]³⁻**:
- Oxidation state of Fe = +3.
- Electron configuration of Fe in +3 state: [Ar] 3d⁵.
- F is a weak field ligand, so no pairing occurs: 3d⁵.
- Hybridization: `sp³d²` (not `d²sp³`).

5. **[CoF₆]³⁻**:
- Oxidation state of Co = +3.
- Electron configuration of Co in +3 state: [Ar] 3d⁶.
- F is a weak field ligand, so no pairing occurs: 3d⁶.
- Hybridization: `sp³d²` (not `d²sp³`).

6. **[Co(C₂O₄)₃]³⁻**:
- Oxidation state of Co = +3.
- Electron configuration of Co in +3 state: [Ar] 3d⁶.
- Oxalate (C₂O₄²⁻) is a strong field ligand, leading to pairing: 3d⁶.
- Hybridization: `d²sp³`.

7. **[MnBr₄]²⁻**:
- Oxidation state of Mn = +2.
- Electron configuration of Mn in +2 state: [Ar] 3d⁵.
- Br is a weak field ligand, so no pairing occurs: 3d⁵.
- Hybridization: `sp³d²` (not `d²sp³`).

### Summary of Findings:
- Complexes with `d²sp³` hybridization:
- [Mn(CN)₆]³⁻
- [Fe(CN)₆]³⁻
- [Co(C₂O₄)₃]³⁻

Thus, **3 complexes** exhibit `d²sp³` hybridization.