Effrontery is rude behaviour that shocks you because the person is so sure of themselves. It is not only being impolite. It is walking in as if nothing were wrong — asking for more money after doing a bad job, talking over a teacher, treating a serious thing as a joke. Speakers use it when they want you to feel the shock: “He had the effrontery to…” The word is formal and a little old in flavour; in everyday talk people say nerve, cheek, or “I cannot believe they had the face to do that.” The old picture is a bare forehead: you do not even cover your face in shame. That is why it sits near front, and why English also has barefaced for a similar kind of shamelessness. You will meet it in novels, newspapers, and angry careful speech, not much in the playground. It names the act or the quality, not the person: we talk about someone’s effrontery, not “an effrontery person.”

厚顏無恥（「居然有臉這樣做」；很書面，口語較常說厚臉皮、太超過）