Correct decreasing order of stability is :
(a) II > III > IV > I           (b) III > IV > I > II
(c) IV > I > II > III           (d) I > II > III > IV

Carbanions are stabilized by EWGs and hence more EWGs more will be the stability of the ion.
Nitro group is EWG because it has Nitrogen with a postive charge.
Methoxy (CH3O) is very strong EDG as it can delocalized  lone pair of oxygen atom in the ring .
Methyl (CH3)group is also electron releasing group however methyl is less stronger electron releasing group than methoxy.
If compare now then Nitro group containing  carbanion is the most stable and  methoxy group containing is the least stable.So order :
(a) II > III > IV > I