Can I include images licensed CC BY-NC 4.0 in a conference paper?

Summary: Is it ok for you to include the CC By-NC 4.0 image in your paper? Yes. Is it ok for the paper to go through a particular process at the conference? Maybe (see below).

The answer to this question is not clear-cut. There is no general agreement as to what constitutes "commercial purpose" with CC licenses. There has been much discussion on the CC pages which has resulted in guidelines, but they are still not black and white.

The best approach is to contact the person who owns the copyright for the image and ask them for permission. That is the non-ambiguous approach. If that is not possible, the next best approach would be to discuss the issue with the conference in question. Depending on how aware they are about licensing issues, they may already have an option in place to address your situation.

A separate issue is the one of copyright transfer. You are free to transfer your own copyrighted content to another body, such as the conference. But you cannot assign another person's copyright to them. Usually there is a line in the copyright transfer agreement that requires you to specify that you own all of the material being assigned to the new owner. Regardless of the outcome above, you do not own the copyright on the image, even if you have permission to use it. These are separate issues. Once again, you should discuss this issue with the conference organizers.

My personal experience has been that many conferences request copyright transfer as a blanket process without realizing that it's often not necessary. When I have contacted such conferences and told them that my work is published under a CC license and that I will NOT assign the copyright to them but WILL give them permission to use it as they see fit, they usually accept and have no problem with it. Sometimes, however, the conferences get stuck on procedure and try to force a single process that doesn't fit modern publishing constraints such as the ones you describe.