This shows man versus nature because Lyddie comes in contact with a bear. The bear makes it nature. This is supported by the following quote: "The bear was too stunned, it seemed, simply to lower his neck and let the kettle fall off." This was on page 3.
This shows man versus man because the gentry on the stagecoach was smoking and staring at Lyddie. Lyddie did not like this, as it caused a problem. This is supported by the following quote: "At first she was mortified, but the longer they rode, the angrier she became. How rude they were, these so-called gentry." This was on page 48.
Lyddie does not know what to do in this situation. She can either listen to her roommates or go to see Diana anyway. This is man versus self because Lyddie is conflicted between her two options, as she thinks about both. This is supported by the following quote: "Lyddie didn't quite know what to do. She had no desire to anger her roommates, but she was quite set on going to see Diana." This is on page 67.