In the phrase "Can you shut up for like once in your life?", the word "like" is used as a filler word. It's often used in casual or informal speech to soften the tone of a statement or to express approximation. In this case, "like" doesn't have a specific meaning but adds emphasis or a conversational tone. It can make the statement sound more relaxed, less direct, or more exaggerated, which is common in everyday speech, especially among younger speakers. So, while "like" isn't necessary for the meaning of the sentence, it's used to make it sound more informal and conversational.