The term 'BEGAN A BROADWAY RUN' can be summarized as the opening of a Broadway show. This is a phrase used to describe the first performance of a musical or play on Broadway, which is a theater district located in Manhattan, New York City. It is the most prestigious form of theater in the United States and is known for its elaborate sets, costumes, and performances. The term 'OPENED' (6 letters) is the past tense of the verb 'OPEN, ' which means to start or begin something.