Thanks for sharing this lovely photo of the John Quincy Adams house, Laurie. It's wonderful that it has been beautifully maintained. Certainly, he is your relative at 6th cousin (6X). Not so much for me at 16th cousin (5X).
However, WikiTree's amazing relationship finder produced this information: I am your 8th cousin (2X) , but through Joanna (Kingman) Holbrook (1624- aft. 1697) not John Adams. But since it's Massachusetts, I then learned Joanna Kingman and John Adams are 8 degrees apart.