What could cause someone to have difficulty climbing maybe 6 stairs?

Difficulty climbing. Many possibilities. It sounds as if you should contact your doctor to find out what is wrong. You will need an examination and probably some tests.
Inactive/injured/etc. If one walks up steps, especially if overweight and/or out of shape, there can be aching in the muscles used most, thigh quadriceps. There can also be balance problems. No matter what age or condition, if someone is having problems walking up steps that typically would not have been a challenge or caused pain, it would be wise to call pcp, heart, physiatrist providers for evaluation/exercise plan.