 Solution

Oxazolination occurs para to oxygen on the ring that does not bear bromine. The product is 2-[4-(4-bromophenoxy)phenyl]-2-Oxazoline, shown in the final panel above. The brominated ring retains its para bromine; the other ring receives the new oxazolinyl group at its open para position.

The diaryl ether oxygen activates both rings toward electrophilic aromatic substitution. On the brominated ring, its least crowded para position is blocked, and bromine also decreases ring reactivity inductively. The unbrominated ring has an accessible para position, favored over its ortho sites by steric effects. This is substitution of an aromatic hydrogen, not displacement of the aryl bromide.

The formula provides a useful consistency check: ${\mathrm{C}}_{12}{\mathrm{H}}_9\mathrm{BrO}$ loses one aromatic H and acquires ${\mathrm{C}}_3{\mathrm{H}}_4\mathrm{NO}$, giving ${\mathrm{C}}_{15}{\mathrm{H}}_{12}\mathrm{BrN}{\mathrm{O}}_2$. It cannot by itself distinguish positional isomers; the directing and steric arguments select the connectivity.