= Solution
Number the <enone> <carbonyl> <carbon> C1, the adjacent <alkene> <carbon> C2 and the ethoxy-bearing <alkene> <carbon> C3. In the \b[bromine-first pathway], the enol-ether-like $\mathrm{C2{=}C3-OEt}$ unit attacks $\mathrm{Br_2}$ at C2, breaking the Br–Br bond. The intermediate has a new C2–Br bond and positive charge at C3, stabilized as an oxonium <chemical resonance> contributor by donation from the ethoxy <oxygen>.
<triethylamine> removes the remaining C2 <hydrogen>. Its C–H bonding pair reforms C2=C3 and neutralizes the oxonium system. The result is \b[replacement of the vinylic C2–H by C2–Br], with the original <enone> and ethoxy group retained. If <bromide> first captures the cationic intermediate, the equivalent vicinal dibromide can eliminate HBr to reach the same product.
The ethoxy group makes this <alkene> sufficiently electron-rich for the electrophilic-addition description. It is important to place <bromine> at C2 and restore the <double bond>, rather than stop at a saturated addition product.
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