I used to think that when I uttered the magic words “I don’t know” my team would think “Glenn is honest and authentic” and “Ok, I’ll relax until someone tells me what I want to know.”
Fool! They might have considered me authentic, but they aren’t impressed and are unlikely to let it go.
Your best approach is to say “I don’t know, we’ll work through it and figure it out together.” Or “I don’t know but here is what I will do to find out and report back to you.”
Next, keep your word.