The correct answer is C. Your shoes need to be cleaned properly.
A. Your shoes are needed to clean properly is incorrect because it is not clear who needs to clean the shoes.
B. You are needed to clean your shoes properly is incorrect because it is not clear who is doing the cleaning.
D. Your shoes are needed by you to clean properly is incorrect because it is not clear what is being cleaned.
The sentence “You need to clean your shoes properly” means that you are the one who needs to clean your shoes, and that you need to clean them properly. The sentence does not say who is going to clean the shoes, but it is implied that you are the one who is going to do it. The sentence also does not say what is going to be cleaned, but it is implied that your shoes are the ones that need to be cleaned.