Answer: My favorite books are J.R.R. Tolkein's Lord of the Rings series, but I love the older classics like Jane Eyre, too. (Tolkein's, series, Jane Eyre, too.)
We are talking about a person's favorite books. This person points out that they love the Lord of the Rings series writen by J.R.R. Tolkein, so this translates in J.R.R. Tolkein's Lord of the Rings series. This eliminates option B's serie's (as the word is series and if we wanted to make it possesive, it would be series'). This also eliminates the last option as they mention J.R.R. Tolkeins without the possesive Tolkein's. Finally, the word "rings" does not require a possesive as it's a plural, so this rules out the third option giving you option A as an answer