Final answer:
The correct answer is to apply the compression sleeves starting at the ankles and work upwards, which helps prevent blood clots by promoting venous return.
Step-by-step explanation:
When caring for a postoperative client following knee arthroplasty who requires thigh-high compression sleeves, the nurse should apply the compression sleeves starting at the ankles and work upwards towards the thighs. This method helps ensure a proper gradient of pressure that aids in preventing venous thromboembolism by promoting venous return and reducing the risk of blood clots. It is important that the compression sleeves fit well and are not too tight, as this could compromise circulation, nor too loose, as they would not provide the necessary compression.