One of the brothers would have told you where their last page is located and how to get it. If you have forgotten, just open their book and click on them again. An impatient brother will remind you.
There is no real 'trick' in entering the pattern in the fireplace. Write down (paper and pencil) the pattern from the book in the library bookcase. It is 8 columns by 6 rows. Go to the fireplace, close the door (by pushing the red button on the left side) and click on the metal plate in front of you where a mark should be. When completed, press the red button again.
Go back to Myst Island -- The end...decision