Concept:
The question tests spatial prepositions and locational adjectives that establish a structural spatial link between two distinct real estate entities: the "Public Library" and "my house". Let's run a structural and grammatical diagnostic check on every single option:
• Option (A) within: "Within" implies inside the boundaries or limits of something (e.g., *within walking distance*, *within the city limits*). Saying a public library is "within my house" is logically absurd because a massive public utility building cannot physically reside inside a private residence.
• Option (B) between: The preposition "between" strictly requires at least two distinct reference points or a plural noun phrase following it (e.g., *between my house and the park*). Since there is only one reference singular noun phrase ("my house"), "between" is grammatically invalid.
• Option (C) far: While "far" expresses long distance, it cannot directly link to an object noun phrase without a supporting preposition. It structurally requires the preposition "from" to function correctly here (e.g., *The Public Library is far from my house*). Left by itself, "far my house" is ungrammatical.
• Option (D) near: The word "near" can function directly as a preposition meaning "at a short distance away from." It effortlessly joins with the target noun phrase without needing any secondary linkers.
Thus, "near" is grammatically valid and logically sound, making the complete sentence: "The Public Library is near my house."