The most stable carboxylate ion among the following is-

1. CH3-C||O-O-

2. Cl-CH2-C||O-O-

3. F-CH2-C||O-O-

4. (F)2-CH-C||O-O-

 
Hint: Resonance effect and inductive effect both working
 
In all the given carbocations, the negative charge is dispersed which stabilises these carbocations. Here, the negative charge is dispersed by two factors, i.e., +R effect of the carboxylate ion (conjugation) and -I effect of the halogens (fluorine).
 
These effect are shown below in the carbocations
(1) 
(2) 
(3) 
(4) 
 
As it is clearly evident from the above structures, that +R-effect is common in all the four structures, therefore, overall dispersal of negative charge depends upon the number of halogen atoms and electronegativity. Since, F has the highest electronegativity and two F-atoms are present in option (4), thus, dispersal of negative charge is maximum in option (4).