He refused to admit his mistake to avoid losing face in front of his colleagues.

losing 是动词 lose 的现在分词形式，lose 的意思是"失去、丧失"。 face 在这里不是指"脸"，而是比喻"面子、尊严"。 losing face 是一个固定短语，字面意思是"失去面子"，即"丢脸、失面子"的意思。