The number of unpaired electrons responsible for the paramagnetic nature of each complex species is calculated as follows:

Complex: $[Fe(CN)_6]^{3-}$

Ion: $Fe^{3+}$

Electronic Configuration: $3d^5$

Orbital Population:

$t_{2g}^{2,2,1}$

$e_g^{0,0}$

Unpaired Electrons: 1

Complex: $[FeF_6]^{3-}$

Ion: $Fe^{3+}$

Electronic Configuration: $3d^5$

Orbital Population:

$t_{2g}^{1,1,1}$

$e_g^{1,1}$

Unpaired Electrons: 5

Complex: $[CoF_6]^{3-}$

Ion: $Co^{3+}$

Electronic Configuration: $3d^6$

Orbital Population:

$t_{2g}^{2,1,1}$

$e_g^{1,0}$

Unpaired Electrons: 4

Complex: $[Mn(CN)_6]^{3-}$

Ion: $Mn^{3+}$

Electronic Configuration: $3d^4$

Orbital Population:

$t_{2g}^{2,1,1}$

$e_g^{0,0}$

Unpaired Electrons: 2

Each complex's paramagnetic nature is due to the specific number of unpaired electrons as indicated above.