challenge vs face up to

challenge

verb
  • To call something into question or dispute. 

  • To question or demand the countersign from (one who attempts to pass the lines). 

  • To dare (someone). 

  • To invite (someone) to take part in a competition. 

  • To be difficult or challenging for. 

  • To object to the reception of the vote of, e.g. on the ground that the person is not qualified as a voter. 

  • To take (a final exam) in order to get credit for a course without taking it. 

  • To make a formal objection to a juror. 

  • To dispute (something). 

noun
  • The act of appealing a ruling or decision of a court of administrative agency. 

  • An antagonization or instigation intended to convince a person to perform an action they otherwise would not. 

  • A bid to overcome something. 

  • The act of seeking to remove a judge, arbitrator, or other judicial or semi-judicial figure for reasons of alleged bias or incapacity. 

  • An act of seeking to have a certain person be declared not legally qualified to vote, made when the person offers their ballot. 

  • The act of a sentry in halting a person and demanding the countersign, or (by extension) the action of a computer system demanding a password, etc. 

  • A summons to fight a duel; also, the letter or message conveying the summons. 

  • A difficult task, especially one that the person making the attempt finds more enjoyable because of that difficulty. 

  • An attempt to take possession; a tackle. 

  • An attempt to have a work of literature restricted or removed from a public library or school curriculum. 

  • The opening and crying of hounds upon first finding the scent of their game. 

  • A judge's interest in the result of a case, constituting grounds for them to not be allowed to sit the case (e.g., a conflict of interest). 

face up to

verb
  • To confront a condition or situation, typically one that is unpleasant or uncomfortable. 

How often have the words challenge and face up to occurred in a corpus of books? (source: Google Ngram Viewer )