= Solution
The <aniline> <nitrogen> attacks the ipso <carbon> bearing <fluorine>. The aromatic $\pi$ electrons shift to give a <Meisenheimer complex>, with negative charge delocalized to the positions ortho and para to the attacked <carbon>. At either nitro <substituent>, that charge can be delocalized further onto nitro <oxygen>. Subsequent <proton> transfer and fluoride elimination restore <aromaticity> and give the diarylamine.
Both the ortho and para <nitro groups> stabilize the addition intermediate in 1-fluoro-2,4-dinitrobenzene. The para-mononitro compound lacks the additional ortho stabilization, so addition is less favourable and generally slower under the stated conditions. This comparison concerns stabilization of the addition pathway; the presence of <fluorine> does not make the reaction an ordinary aliphatic <SN2 reaction>.
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