The correct active form of the given sentence is You should have placed the books on their proper shelves.

The sentence The books should have been placed on their proper shelves is in the past perfect subjunctive mood, which is used to express a wish or regret about something that did not happen. The active voice of the sentence is formed by putting the subject of the passive sentence before the verb and removing the verb "to be." In this case, the subject of the passive sentence is "the books" and the main verb is "place." So, the active form of the sentence is You should have placed the books on their proper shelves.

The other options are incorrect because:

• You will have placed the books on their proper shelves. is in the future perfect tense, while the original sentence is in the past perfect subjunctive mood.
• You should place the books on their proper shelves. is in the present tense, while the original sentence expresses a wish or regret about something that did not happen in the past.
• You need to place the books on their proper shelves. is in the imperative mood, which is used to give commands or make requests.
• The books need to be placed on their proper shelves. is in the infinitive form, which is not a complete sentence.