It can be helpful to restate the framing of the question /problem beforehand to clarify, reduce room for misunderstandings, communicate that you care enough to get it right, and also buy yourself time to maybe come up with an answer on the fly. Sometimes an extra minute or two is enough to come up with something good.

I don't know, but I'll find out and get back to you." is fine. If you're really anxious, you can say "I want to give you a good answer, so let me think on this and get back to you. Is an email/slack convenient for you or should we reconvene at <datetime>?"