A simile is a figure of speech that presents the likeness between two
unlikely things and contains the words 'like' or 'as'. For example, as
smooth as butter, light like a feather and so on. In the given sentence the "sister" is compared with a rake (long, thin broom) because she hadn't been eating well. The phrase "thin as a rake" draws a likeness with the sister and a rake, both being very thin, hence it's a simile and option D is correct. "My sister" is the subject of this sentence, it's not a figure of speech (simile) hence option A is incorrect. "Hasn't been eating" is a verb phrase in the present perfect continuous tense; it's not a simile hence option B is incorrect. "Rake" is a noun on its own, it does not perform the function of a simile without 'as', hence option C is incorrect.