Hello! Can we use “face” as a synonym of “come across” or not?
For example: I faced him yesterday.

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Answer

"I faced him yesterday" sounds like you were his opponent in a game, fight, argument, etc.

I would just say it like this:

I saw him yesterday.

Answer

Not exactly. When you say "I faced him", it sounds like you stared at him or maybe you confronted him somehow. 
You could say "I came face to face with him", that would be semantically related to "come across".