The speakers in the book refer to the magical devices used by the Ministry of Magic to broadcast the propaganda of Minister Cornelius Fudge. These devices are controlled by magic and their "destruction" is metaphorical.
Here are the ways the speakers are "destroyed" in the book:
* Disbelief: Harry and his friends actively resist believing the messages broadcast by the Ministry, effectively rendering the speakers useless in terms of influencing their thoughts.
* Truth and Evidence: Dumbledore and the Order of the Phoenix use real events and evidence to counter the lies propagated through the speakers, ultimately discrediting the Ministry's narrative.
* Word of Mouth: Through direct communication, spreading their own stories, and sharing the truth, Harry and his allies create a network of information that eclipses the Ministry's attempts to control the narrative.
So, while the speakers themselves aren't physically destroyed, their effectiveness is undermined by the characters' actions and the power of truth.