Can you sail from Sopers Hole to Anegada and back comfortably on a 6 day sail? We will be sailing a 580 Cat with a Captain. We definitely want sailing time on the water. We plan on staying one night at Norman Island, Virgin Gorda, Anegada, Scrub (Prickly Pear or Beef), Jost Van Dyke and finally Sopers Hole. Thank you in advance for your advice.

Doable. The key is getting synched up on a weather window.
With 6-days you either have it and you can go, or you're skipping it this trip.
$0.02 - You're really shorting yourself if you sail to Anegada in the morning, only have the afternoon to explore, and then leave the next day. 1-1/2 to 2 days really makes it worth while.

Depending on the winds, you could actually sail from Sopers hole to Anegada in a single long day of sailing. Recommend leaving from the north sound of Virgin Gorda early am and arriving on Anegada early so you can spend a whole day. One could definitely spend a week at nearly any place in the BVI, and Anegada is no exception. A single day on Anegada is great and will allow you to see alot, and leave you wanting more...a great reason to come back. Google sample itinerary BVI to see some typical routes, stops, etc. We've done the BVI many times now and being open to changing plans/being flexible and heeding the recommendations of the Skipper are a good way to go. You will have a great time!