The phrase "not let out a peep" means to remain completely quiet or silent. There are many synonyms that can be used to convey this meaning, including "not make a sound," "not utter a word," "not whisper a syllable," "mute," "silent," "still," and "hushed." Other synonyms include "quiet as a mouse," "dead quiet," "pin drop silence," and "not a breath of air." These synonyms are useful when trying to describe a situation where absolute silence is required, such as during a movie or a play, or to portray a character who is unable to cry out for help.