Hi Diane!
Thank you for bringing your question to the Disney Parks Moms Panel!
There is a path you can take from
Disney's Hollywood Studios to
Epcot if you want to walk. I would say that all together it would be somewhere around a mile and a half between the two. It's an easy walk, but could be tiring after a day in the parks.
Another option is to take the
Friendship ferry boats between the two parks. The boats will make stops at the Swan and Dolphin Resort dock, the Boardwalk Inn dock and the Beach/Yacht Club dock before arriving at Epcot. As a family with competitive teenage boys, we often hold "races" to see who can get between the two faster...the walkers or the boaters! If you walk at a fast pace, you can usually beat the boats, but it's not nearly as relaxing!
I hope this helps! Please let me know if you have any other questions.
~Lori