arrange the following in nucleophile strength :

c₆h₅o^- , ch₃coo^- , ch₃o^- , oh^-

The order would be as follows :
CH₃O^- >​ OH^- >​ CH₃COO^- >​ C₆H₅O^-
In case of phenoxide and carboxylate, the negative chrge is delocalised by resonance hence it not available for the nucleophilic attack easily.
Hydroxide ion (^-OH) is weaker nucleophile than alkoxide ion (​^-OR) because electron density at oxygen in case of ​ ^-OH ion is less as in case of ​ ^-OR. Alkyl groups shows electron donnating inductive effect (+I Effect) due to which electron density increases on oxygen which makes ​^-OR stronger nucleophile than ​^-OH ion.