Catalysis of the reaction: 3',4',5,6-tetrahydroxy-3,7-dimethoxyflavone + S-adenosyl-L-methionine(1+) = 3',4',5-trihydroxy-3,6,7-trimethoxyflavone + S-adenosyl-L-homocysteine + H+.
flavonol 6-methyltransferase activity