This is man VS nature because Lyddie stares down a bear. Pg: 2 "Lyddie glared into the bear's eyes, daring him to step forward into the cabin."
Man VS Man because Lyddie, Tryphena, and the Mistress all got in an argument because Tryphena let Lyddie visit her cabin. Pg: 44 "Lyddie went past the angry woman without a word,"
This is man VS self because Lyddie is contemplating what would happen if she saw a slave. Pg: 33 "In a way, she'd like to see one, but what would she do? What would she say? And supposing it was a fugitive, what then? One hundred dollars!"