The correct option is C Browns'
Let’s examine the sentence: “The ____ house is on Park Street.” The usage of ‘The’ indicates that the following blank cannot have the name of an individual. This rules out using the Option A as answer. So, the sentence seeks to show that the house belongs to a family. It needs a family name in possessive case. The possessive case shows ownership. With the addition of ’s (or sometimes just the apostrophe), a noun can change from a simple person, place, or thing to a person, place, or thing that owns something. Option C is the only other option having apostrophe to show the possessive case and hence, that is the answer.