Answer: The right answer is "a machine that separated cottonseeds from the plant fibers."
Explanation: Although the way the different options have been presented is confusing, it is possible to say that the words that form an appositive are those that define the cotton gin, or provide more information about it, forming, with it, a syntactic unit, namely, "a machine that separated cottonseeds from the plant fibers." An appositive is a noun that follows, or is right behind, another noun, and that identifies it further. This is why it is said that the second noun is "in apposition to" the first noun, since it is adjacent to it - aposition comes from the Latin word appositio, -ōnis (ad meaning "near" and positio meaning "placement").