The clause from the drop-down menu that correctly punctuates the sentence is B, "who live down the street". This sentence is a restrictive relative clause which is introduced by the relative pronoun "who" and it is not set off with commas since its information is relevant to the meaning of the sentence. It identifies the children as those who live down the street, so it provides essential information about the noun to which it refers and cannot be removed without altering the sentence's meaning.
My best friend Sara agreed to babysit her youngest aunt's children who live down the street.