The main conflict in this book is resolved through Karana's resourcefulness and her courage.
The main conflict in this book is the conflict between Karana and nature (and a few humans). She is trying to survive all alone on the island. The only way that she can survive is by being very brave and very clever. For example, we see both of these qualities in her interactions with the pack of dogs that kills her brother. We see her bravery and resourcefulness both as she devises and carries out a way to kill the dogs in revenge for her brother's death. It is also rather resourceful of her to tame Rontu to help give her the sort of emotional support she needs to survive on her own.
Through her resourcefulness and courage, Karana survives this and many other dangers. This is how the main conflict in the book is resolved.