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One of the spectators disrupted the proceedings by shouting loudly.
Literal
Spectators [possessive-の] one-person [subject-が] loud-voice [object-を] raised-[sequential-て] proceedings [object-を] obstructed
傍聴人 is specifically a spectator at a courtroom, diet session, or public hearing — not a general audience member (観客). 議事進行 is a formal compound: 議事 (proceedings) + 進行 (progress) = 'progression of proceedings'. 妨げる is to obstruct or hinder. The て here connects two sequential actions: shouting and (thereby) obstructing.