What are the main conflicts in the book from chapter 9 to 12, and what type of conflicts are they?Are these examples of person vs. person, person vs nature, or person vs himself?
I would have to say that the main conflict toward the end of the book "Lord of the Flies" is man-versus-man, with a strong twinge of man-versus-nature thrown in for spice. Interestingly, you can make a case for "man-versus-himself," though I think that applies a bit better to the middle of the book.
Let me explain:
The end of the book is dominated by the "hunt" that occurs between Ralph and Jack's savages. This occurs mostly in chapters 11 and 12. This is clearly "man-versus-man." In addition, this is the section in which Piggy is killed, another clear example of this type of conflict.
In chapter 12 we see the island on fire, and this becomes a major obstacle not only for Ralph but for Jack n' crew as well (though they don't seem to realize it.) This is a great example of "man-versus-nature" because the fire is represented as a force of nature.
In a lot of ways the last four chapters are also a great game of "man-versus-himself," though again I think there are stronger examples toward the middle of the story. There is still plenty going on in the last four to make it fit. Look at the transformation of the main characters from innocence to chaos (especially Jack and Ralph.) Earlier, as well, we see Simon slowly losing his mind while talking with the pig head.
These are just a few ideas, but I think they are the major ones. Good luck!