In cases where a metal ion like, Fe(III), Cr(III), Pt(II) is made to react with a ligand species like oxalate, CN-, CO etc and it forms a complex then, How do we determine whether 6 ligands will be coordinated to the central atom(i.e. in case of octahedral) or 4 ligands will be coordinated (as in tetrahedral or square planar arrangement) ?
From your question, I suppose you do not know about crystal field theory. To properly understand how and why certain complexes are octahedral and other ones are tetrahedral you need to fully understand this theory. You can find information in Greenwood and Earnshaw, Chemistry of the Elements. A more detailed info about the theory is in Theory of Groups in Chemical Applications of Group Theory of Cotton.
I will explain the basis concept here. The isolated ion has a spherical symmetry, then all the microstates for a specific electronic configuration have the same energy. The ligands can be imagined as a source of electric potential. This field alters the symmetry, than the microstates have not all the same energy. In particular, the 5d orbitals will not have the same energy in presence of the ligands because they are shifted up and down. A degeneracy remotion, as always in QM, will alter the symmetry of the system, that is the structure will change. Then the geometry of a complex depends upon:
- the nature of the metallic center
- the oxidation state of the metallic center
- the nature of the ligands ($\pi$-basic, $\pi$-acid, $\sigma$-donor and so on).