Page 1 : "Don't nobody yell," she said softly. "Just back up slow and quiet to the ladder and climb up to the loft." This is man vs nature because it's Lyddie against a bear which is a human being interacting with an animal that is part of nature.
Page 44: "Your dismissed! the woman said." This is man vs man because Lyddie is fired from the tavern which makes it two people interacting with each other.
Page 65: "Lyddie was a farm girl. She took pride in her strength, but it took all of her might to yank the metal lever into place." This is man vs self because Lyddie continues to doubt herself about the work she has to do.