as a person who stutters there are some things I would like when someone wants to talk about my stuttering problem 1. Breach the topic when you think the other person is in a good mood and make sure they are comfortable with it. 2. do you have a problem with them stuttering? I am just gonna assume that you are pretty nonchalant about it. Make yourself clear that you do not mind it and they can openly talk without feeling judged 3. If possible, do not finish our sentences for us. Just nod sometimes whenever they are stuck on a block 4. Don't judge your co-worker, even if you think you are hiding it well, trust me you are not, your eyes spells it for you