This sentence deals asks you about an appositive phrase - a phrase that redefines or gives more information about about a noun in a sentence.
In this sentence, "poets" is the noun, and the names of the poets - "Percy Bysshe Shelley, Lord Byron, and John Keats" made up the appositive phrase.
Appositive phrases need additional punctuation in the sentence, to set them apart from the rest of the sentence. You can generally use sets of commas or dashes, or other types of punctuation, such as a colon, to set the phrase apart. In this question, you are being asked to use dashes specifically.
With all of the above information in mind, now that you know 1) what an appositive is and 2) how an appositive phrase can be punctuated, we can conclude that your sentence should look like this:
The Romantic poets - Percy Bysshe Shelley, Lord Byron, and John Keats -influenced Rachel's poem for class.
So, the correct answer would be C. - the dashes should go before "Percy" and after "Keats."
