The phrase "hast egg on one face" means to be embarrassed or ashamed about something one has done or said. There are many phrases that can be used synonymously with this expression. For example, "eating crow" means to admit that one was wrong and apologize, often due to a public humiliation. "Putting one's foot in their mouth" means to say or do something embarrassing that one regrets. "Making a faux pas" suggests a social blunder or misstep. "Feeling sheepish" reflects a sense of embarrassment or guilt. Whatever the case, it is important to learn from one's mistakes and move forward with a renewed sense of humility and grace.