The correct option is
B To swallow one's pride and admit that one is wrong
The given phrase means 'To face humiliation and subsequently apologise for a mistake'.Option C is correct. 'To swallow one's pride' can be interpreted as 'facing humiliation' and 'to admit one is wrong' means apologising. Thus, it has the required meaning.
Options A, B and D are incorrect. They do not have the required meaning.