In octahedral complex `Ma_(2)b_(2)cd`, total number of steroisomers is

Explanation

To determine the total number of stereoisomers for the octahedral complex \( Ma_2b_2cd \), we need to analyze the arrangement of the ligands around the central metal atom \( M \).

### Step-by-Step Solution:

1. **Identify the Coordination Number and Geometry**:
- The complex \( Ma_2b_2cd \) has a coordination number of 6, which corresponds to an octahedral geometry.

2. **Determine the Types of Ligands**:
- The complex consists of two types of bidentate ligands \( A \) and \( B \), and two monodentate ligands \( C \) and \( D \).

3. **Geometric Isomerism**:
- In octahedral complexes, geometric isomers can arise from different arrangements of the ligands. For \( Ma_2b_2cd \), we can have:
- **Facial (fac)**: where the two \( A \) ligands and the two \( B \) ligands occupy adjacent positions.
- **Meridional (mer)**: where the two \( A \) ligands and the two \( B \) ligands occupy positions such that they are opposite each other.

4. **Counting Geometric Isomers**:
- For \( Ma_2b_2cd \):
- **Facial Isomer**: The arrangement can be \( AABBCD \).
- **Meridional Isomer**: The arrangement can be \( AABCD \).
- Thus, there are 2 geometric isomers.

5. **Optical Isomerism**:
- Optical isomers arise when a complex lacks a plane of symmetry.
- The facial isomer can have optical isomers because it lacks symmetry.
- The meridional isomer typically has a plane of symmetry and does not exhibit optical isomerism.

6. **Total Stereoisomers**:
- From the facial isomer, we can have 2 optical isomers (enantiomers).
- From the meridional isomer, we have 1 non-optical isomer.
- Therefore, the total number of stereoisomers is \( 2 \) (from facial) + \( 1 \) (from meridional) = **3 stereoisomers**.

### Final Answer:
The total number of stereoisomers for the octahedral complex \( Ma_2b_2cd \) is **3**.