Answer:
The sentence that is punctuated correctly is the following one: My sister, who is a waitress at Billy's Big Burger Shack, is sixteen years old.
Step-by-step explanation:
The sentence above is a nonessential relative clause. As such it is separated from the rest of the sentence with commas because it does not provide relevant information to complete the meaning of the sentence. If the relative clause was removed, the meaning of the sentence would be left unchanged (see 1).
1) My sister is sixteen years old.