Ms Alvarez ____ chemistry at our school for two years before she moved abroad.

Explication

The clause describes a stretch of time that closed when she moved abroad, so the past simple is required, and teach becomes taught. The verb spends no second form on the perfect: taught is also what follows have, so she has taught here for years reuses the very same word. Teached regularises a verb whose past is built by vowel and ending change instead.