The number of paramagnetic complex among $$[FeF_6]^{3-}$$, $$[Fe(CN)_6]^{3-}$$, $$[Mn(CN)_6]^{3-}$$, $$[Co(C_2O_4)_3]^{3-}$$, $$[MnCl_6]^{3-}$$ and $$[CoF_6]^{3-}$$, which involved $$d^2sp^3$$ hybridisation of metal is ______.

In an octahedral complex the possible hybridisations are:
- $$d^2sp^3$$ (inner-orbital, produced only when the ligand field is strong enough to force electron pairing in the $$\,(n-1)d\,$$ shell)
- $$sp^3d^2$$ (outer-orbital, produced with weak-field ligands; no pairing in the $$\,(n-1)d\,$$ shell)

Hence the required complex must simultaneously
(i) contain a strong-field ligand set so that $$d^2sp^3$$ hybridisation becomes possible, and
(ii) still possess at least one unpaired electron so that it is paramagnetic.

Step-wise examination of every complex:

Case 1: $$[FeF_6]^{3-}$$
Fe is in the $$+3$$ state ⇒ $$d^5$$.
$$F^-$$ is a weak-field ligand ⇒ high-spin $$sp^3d^2$$ hybridisation.
Hybridisation condition fails ⇒ reject.

Case 2: $$[Fe(CN)_6]^{3-}$$
Fe$$^{3+} : d^5$$.
$$CN^-$$ is a strong-field ligand ⇒ electrons pair in the $$\,(n-1)d\,$ orbitals giving the low-spin configuration $$t_{2g}^5\, (1$$\text{ unpaired}$$)$$.
Hybridisation: $$d^2sp^3$$ (inner-orbital).
Paramagnetic (1 unpaired).
✓ Satisfies both conditions.

Case 3: $$[Mn(CN)_6]^{3-}$$
Mn$$^{3+} : d^4$$.
$$CN^-$$ strong-field ⇒ low-spin $$t_{2g}^4$$ (2 unpaired).
Hybridisation: $$d^2sp^3$$.
Paramagnetic (2 unpaired).
✓ Satisfies both conditions.

Case 4: $$[Co(C_2O_4)_3]^{3-}$$
Co$$^{3+} : d^6$$.
Oxalate $$(C_2O_4)^{2-}$$ is a reasonably strong field for the highly charged Co$$^{3+}$$ ion ⇒ low-spin $$t_{2g}^6$$ (all electrons paired).
Hybridisation: $$d^2sp^3$$, but the complex is diamagnetic.
Fails the paramagnetism requirement ⇒ reject.

Case 5: $$[MnCl_6]^{3-}$$
Mn$$^{3+} : d^4$$ with weak-field $$Cl^-$$ ⇒ high-spin $$sp^3d^2$$.
Hybridisation condition fails ⇒ reject.

Case 6: $$[CoF_6]^{3-}$$
Co$$^{3+} : d^6$$ with weak-field $$F^-$$ ⇒ high-spin $$sp^3d^2$$ (4 unpaired).
Hybridisation condition fails ⇒ reject.

Only two complexes, $$[Fe(CN)_6]^{3-}$$ and $$[Mn(CN)_6]^{3-}$$, satisfy
(i) $$d^2sp^3$$ hybridisation and
(ii) possession of unpaired electrons.

Therefore, the required number of paramagnetic $$d^2sp^3$$ complexes is $$\mathbf{2}$$.