Student or Learner
After months of research, Mr. Kim has (yet/finally) to come to a conclusion on the feasibility of international expansion.
I think both can be used in this sentence but the answer is 'yet'.
I think the idea behind the question is that the normal answer for the second option would be finally come if it had the same meaning. I agree with Bhaisahab that both could be used, with different meanings, so it's most likely to be a clumsy question.
You would need to delete the "to" that comes after the blank for "finally" to work.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
NOT A TEACHER
This is how I view your two versions:
1. After months of research, Mr. Kim has yet to come to a conclusion. = He has not reached a conclusion yet.
2. After months of research, Mr. Kim has finally come to a conclusion. = He has reached a conclusion.
If this was a test question, then you know that the only correct answer would have to be "yet," for you cannot say "has finally to come."
HAVE A NICE DAY!