[Big-Daddy]

How do I find all the different geometric and optical isomers of a general octahedral complex ion with only monodentate ligands? I know well the method for finding geometric isomers in a square planar complex: any pair of ligands positioned diagonally to each other are opposite and their positions freely rotatable. However, I need a similar method to apply for geometric isomerism in octahedral complexes (and preferably, geometric isomerism in general) and also optical isomerism which I don't know how to include when in conjunction with geometric.

[Archer]

You need to draw them or build them with a modelling kit.

Remember that optical isomers are mirror images of one another but not superimposeable on one another.

How many different ligands do you have?

[Vidya]

In case of octahedral complexes of the type MA3B3 like [Co(NO2)3(NH3)3] exists as fac or mer isomer.Facial -when three identical ligands are on the same face of the corners of the triangular face .Meridional or mer isomer when three ligands  are on three corners of the square planar.Octahedral complexes with bidentate or multidentate  ligands can only show optical isomers.

[Big-Daddy]

In case of octahedral complexes of the type MA3B3 like [Co(NO2)3(NH3)3] exists as fac or mer isomer.Facial -when three identical ligands are on the same face of the corners of the triangular face .Meridional or mer isomer when three ligands  are on three corners of the square planar.Octahedral complexes with bidentate or multidentate  ligands can only show optical isomers.

Thanks this is very important to keep in mind. However, for the isomers with all monodentate ligands, I need to know for other configurations than just Ma₃b₃, how to find the isomers for those.

[Vidya]

with Ma2b4 type - you need to check a and if they are on the same side of the plane then it is cis and if on opposite corners then it is trans
I don't think any geometrical isomers are there with Mab5 type