Atomic number of Cr and Fe are respectively 24 and 26, which of the following is paramagnetic with the spin of electron : -

$[Cr(CO)_6]$: Cr(0), $3d^6$ with strong field CO; all electrons pair up ($t_{2g}^6$), diamagnetic.
$[Fe(CO)_5]$: Fe(0), $3d^8$ with CO; all paired, diamagnetic.
$[Fe(CN)_6]^{4-}$: $Fe^{2+}$, $3d^6$ with strong field $CN^-$; low spin $t_{2g}^6$, diamagnetic.
$[Cr(NH_3)_6]^{3+}$: $Cr^{3+}$, $3d^3$. Three electrons occupy the three $t_{2g}$ orbitals singly ($t_{2g}^3$), whatever the ligand strength. So it has 3 unpaired electrons and is paramagnetic ($\mu \approx 3.87$ BM).
So $[Cr(NH_3)_6]^{3+}$ is paramagnetic.