Aromatic Apparent Substituion Reaction Mechanism
The question is slightly misleading. It is usually referred to as a substitution; nucleophilic aromatic substitution to be precise; but it is actually an addition-elimination. What the question is trying to say is that it is not a regular $S_N1$/$S_N2$ substitution (which I think you correctly realised anyway).

The mechanism involves attack at the carbon attached to the bromine to form an intermediate anion which is stabilised by the electron withdrawing acetyl group, para to the site of attack.

I'll let you draw the arrows and come up with a complete mechanism.