Keep your answer simple and avoid over dramatizing any event. Speaking negatively about others will always look unfavorable towards you. Telling the interviewer that you get along with everyone is not an appropriate or believable response either. Focus on a time when your work style was different than another person but perhaps you still had to successfully complete a project together. Discuss, in a positive tone, how you made it work!
"Last month I had to collaborate on a project with another project manager who works very differently than I do. I find timely client follow up to be incredibly important and this particular PM seemed to be more relaxed with that aspect. I continued to work how I always do but did ask this PM a couple of times to communicate more frequently with our client in order to make the collaboration smoother. I fully understand that not everyone will work in perfect synergy and that is okay. It's what makes everyone unique. There is always a professional workaround available - sometimes you just have to approach the situation head-on but in a respectful way."
"We had a team member who constantly was late to meetings and missed deadlines. They were a critical part of our team, so I approached them privately to understand what was going on that was preventing them from working well with the team and offered any support to get them there."
"I worked with a coworker who scoffed at other coworkers ideas and loudly proclaimed that he was the smartest person in our office. I approached him and our supervisor about the attitude and insults. It turned out that he did not want to work in our division and an amicable transfer was made."
Sales answer example
"I often have to work across departments with a project manager who approaches problems, and people, very differently than I do. She is more comfortable taking an indirect, apologetic route whereas I prefer to tackle things head on and with gusto. At first, it was a challenge to get both of our ideas fully understood by the other, since our communication styles are so different. However, once we both mapped out our visions in our own ways, we were able to leverage each of our strengths to build on the other's ideas.
In the end, not only was the project completed ahead of time and well received, but also I learned some communication techniques from her that I still use to this day."
Retail answer example
"There will always be coworkers that are difficult to deal with, it's part of what keeps things interesting. Much of my job is based on finding common ground with people and relating to them in a positive way, and this does not end with the customer, but rather is an important part of dealing with coworkers, whether in a management position or not.
As far as obnoxious behavior, I ignore it as much as possible. There is a point where I will make it clear in a kind, but firm, way that the topic at hand is bothersome or inappropriate and ask that it not be discussed in my presence, or at all, depending. However, I just try to take people as they are see the good in them, even if they drive me nuts most of the time."
Teacher answer example
"One of the classroom teachers and I have conflicting styles. She likes her students to be quiet, I like them up and moving, and I hold my loud class within her classroom! I know I drive her nuts and it's gone so far as having the students tell me, "Mrs. P said we need to bring it down a notch". While I am sure to be respectful of her and her classroom, and leave the students and items in the class exactly where I found them, and try to help bring them down a little before I leave. However, since I don't tell her how to teach, so I prefer she doesn't send messages through the students to me. I hope that she will see that the kids are better behaved after Spanish, since they got all of their wiggles out then. If not, I can only keep doing my job how I best see fit and remain respectful, but respectfully, and silently, disagree with her teaching philosophy."