S-adenosyl-L-methionine-dependent methyltransferase that catalyzes the methylation of the guanosine nucleotide at position 6 (m2G6) in tRNA. guanosine(6) in tRNA + S-adenosyl-L-methionine = H(+) + N(2)-methylguanosine(6) in tRNA + S-adenosyl-L-homocysteine Belongs to the methyltransferase superfamily.