Rema spent 6 days reading her book, completing the same fraction of the book each day, if she read a total of 8/9 of her book after 6 days, what fraction of the book did she read each day?

Since it took 6 days to read 8/9 of the book, then just divide 8/9 by 6.
Taking an extra step, multiply the numerator and denominator by 6 which gets you 48/54. 
Now you can divide 48 by 6 which is 8.
Your answer would be 8/54 so just simplify that and you will get 4/27.

*You can easily check your answer by multiplying it by 6.*
(4/27) × 6 = 24/27 ⇒ 8/9