 Solution

tert-Butoxide removes the acidic hydrogen from $\mathrm{PhCH}(\mathrm{OPh})\mathrm{CN}$. The resulting carbon anion is stabilized by the nitrile group and the phenyl substituent. It attacks the aromatic carbon bearing fluorine, giving a Meisenheimer addition intermediate. Ring pi bonds shift toward the para nitro group, where the negative charge can be delocalized onto oxygen.

Loss of fluoride restores aromaticity and gives $\mathrm{p}-\mathrm{N}{\mathrm{O}}_2{\mathrm{C}}_6{\mathrm{H}}_4-\mathrm{C}(\mathrm{Ph})(\mathrm{OPh})\mathrm{CN}$. This is an addition–elimination nucleophilic aromatic substitution. The phenoxy group remains attached to the incoming carbon. The ipso aromatic carbon already has a leaving group, so rearomatization can occur by fluoride departure without removing phenoxide. Acid workup neutralizes residual anions; it is not a separate step that replaces the aryl fluoride.