Ashelf at a bookstore displays 27 books. of these 27 books, nine of the books i nonfiction books. the store owner add six new books fiction books to the shelf and once the ratio of the fiction books to nonfiction books to remain the same. what is the total number of nonfiction books that the store should display, after the new fiction books are at it?

You're told that there are 27 books total and 9 of them are nonfiction. That means 27-9 = 18 books are fiction.

The ratio of fiction to nonfiction is 18 fiction to 9 nonfiction = 2 fiction to 1 nonfiction. That means for every nonfiction book, there are two fiction books. 

If 6 new fiction books are added, you will have 18+6 = 24 fiction books. To keep that 2 fiction to 1 nonfiction ratio, that means you should have 24/2 = 12 nonfiction books. 

You currently have 9 nonfiction books displayed, so 3 more nonfiction books should be added to display a total number of 12 nonfiction books.