Final answer:
The correctly written nursing order for the given diagnosis of acute pain related to deep vein thrombosis is to maintain complete bed rest with the affected leg elevated on two pillows at all times.
Step-by-step explanation:
The correct nursing order for the diagnosis of acute pain related to deep vein thrombosis (DVT), as manifested by redness, swelling, warmth, and positive Homans' sign is: b) Complete bed rest with right leg elevated on two pillows at all times. This order directly addresses the issue of reducing the effects of gravity on blood flow in the vein, aiming to decrease venous pressure and swelling, which can help alleviate acute pain caused by DVT. Other options such as assessing pain levels and vital signs are important but are not specific enough for the stated diagnosis and manifesting symptoms.