We've all been there. Your client has said something inflammatory, or has made an unreasonable demand. Perhaps you've even been shouted at. Yuck.
Take a beat. Breathe a little. Actually, focus on that breath. Feel the air move up your nose and down your throat. Notice the pause before you breathe back out, and follow the breath back out. Or maybe you are more tuned in with noticing your chest or abdomen rising and falling with the breath. No problem. Just allow your focus to follow your breath for those few short seconds.
This small distraction can help to bring you back to centre. The unhappy experience will pass, but in the meantime, some kind of action must be taken. But you don't need to strongly react.
Try listening. Ask for clarification. Show that you care and even empathize. Repeat back what you heard so your client knows that you have listened.
This person is suffering. They either want something they don't have, or they don't want something that they have gotten. This is always how suffering arises. It's not always logical. Angry or upset people are often so overcome by their emotions that they really aren't thinking clearly.
You don't need to fall into that trap. If you are not sure how to help in that moment, simply let your client know that you did understand and that you do care. Say you would like some time to help find a solution. It's fair to let your client know that you would like some time, and ask if you can reconvene the conversation the following day, or at another mutually convenient time. You can also make it clear that you want to find a solution together, one that you'll both find acceptable. This as an opportunity, not a problem.
Assure your client that you will return to this issue at the time agreed upon. Once you have some time to think it over, you'll know your client is doing the same. When you meet again, it's understood that a resolution is wanted by both parties. By this time, everyone will be calmed down and far more reflective, resulting in a more positive discussion.
When you meet again, take that breath, and remember to smile. It's always easier to work out a problem when people see the humanity in one another. You've got this.