The correct stability order for the following free radical is

I) 

 

 

 

II)

 

 

 

III)

 

 

 

IV)

In compound (I), there are two resonating structures because free radical and one double are in conjugation. This enhances the stability of the molecule.

In compound (II), there is extended conjugation because one free radical and two double bonds are in conjugation. Therefore, compound (II) has the maximum stability.

In compound (III), there is a tertiary free radical which is stable by hyperconjugation but its stability is lesser than compound (I) and compound (II).

The hybridization of a double bonded carbon atom is sp². As it has more s%, this implies that it is more electronegative than sp³ hybridized carbon atom. Therefore the stability of compound (IV) is least among the given options.

Order of stability is II>I>III>IV.