【Meet】 ,  【face】 ,  【encounter】 ,  【confront】  can all mean to come across or to run into someone or something 【face】 -to- 【face】 or as if 【face】 -to- 【face】 .

【Meet】 fundamentally implies the action of two or more persons or things which from different directions come across each other by design or by accident; often it implies nothing more.

Beyond this, the word may suggest such actions or intentions as finding, experiencing, or dealing with successfully.

【Face】 may imply nothing more than a standing or a meeting 【face】 -to- 【face】 (as of persons or things that merely present their faces or their fronts to each other), but it more often emphasizes the act or intention of one who with courage or resolution or confidence, or with effrontery, or with desperation, looks upon or meets another person or thing.

【Encounter】 in its earliest and still not uncommon sense implies mutual hostility or active conflict. There has, however, been a progressive weakening of this implication, so that the word more frequently implies a running up against something that presents a difficulty, hardship, or obstacle.

Often, even this notion of difficulty or hardship in turn is lost and the term means nothing more than  【meet】 , especially by chance or unexpectedly.

【Confront】  more clearly than the other terms stresses the unavoidable  【face】 -to- 【face】 nature of the meeting and often also carries a strong implication of a resolute intent or firm determination to clarify an issue or settle a difficulty through such meeting.