Which of the following has longest $C-O$ bond length? (Free $C-O$ bond length in CO is $1.128\mathring{A}$).

As negative charge on metal carbonyl complex increases, back $\pi$-bonding increases and hence bond length of C- O bond increases while bond length of metal-carbon bond decreases.
Hence, ${\left[Fe{\left(CO\right)}_4\right]}^{2-}$ has longest C-O bond length among the given complexes.
The correct order of bond length of the given complexes is
${\left[Mn{\left(CO\right)}_6\right]}^{+}<\left[Ni{\left(CO\right)}_4\right]<{\left[Co{\left(CO\right)}_4\right]}^{-}<{\left[Fe{\left(CO\right)}_4\right]}^{2-}$