Matching 2 groups of people by a set of preferences

Not sure if this is an algorithm question or asking for best package. Sorry, no reprex:

I have 2 lists:

  1. List of people who want to be mentored with location, department and preference rating of 10 skills they want mentoring on. Along with their OK with remote mentor.
  2. List of people (about half as many) who are prepared to mentor. Along with location, department and preference rating of the 10 skills

I have been asked to get a best fit. I don't think it is a linear optimisation problem. Any ideas?
On approach is to find solutions to the hardest fits and successively solve the next hardest fits.

New one to me!

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