Alkyl halide gives the nucleophilic substitution reaction with nucleophile. The rate of reaction depends upon the nucleophilicity of the alkyl halide.  Hence, the nucleophilicity order of the given nucleophiles is  $\left(\mathrm{IV}\right) {\mathrm{CH}}_3{\mathrm{O}}^{\Theta }>\left(\mathrm{III}\right){\mathrm{OH}}^{-}>\left(\mathrm{I}\right) {\mathrm{PhO}}^{-}>\left(\mathrm{II}\right) {\mathrm{CH}}_3{\mathrm{COO}}^{-}$.

${\mathrm{CH}}_3-{\mathrm{CH}}_2-\mathrm{Br}+{\mathrm{Nu}}^{\Theta }\to {\mathrm{CH}}_3-{\mathrm{CH}}_2-\mathrm{Nu}+{\mathrm{Br}}^{\Theta }$

Hence, the decreasing order of the reaction rate with nucleophile is $\left(\mathrm{IV}\right) {\mathrm{CH}}_3{\mathrm{O}}^{\Theta }>\left(\mathrm{III}\right){\mathrm{OH}}^{-}>\left(\mathrm{I}\right) {\mathrm{PhO}}^{-}>\left(\mathrm{II}\right) {\mathrm{CH}}_3{\mathrm{COO}}^{-}$.