Transfers the sialyl group (N-acetyl-alpha-neuraminyl or NeuAc) from CMP-NeuAc onto glycoproteins and glycolipids, forming an alpha-2,6-linkage. Produces branched type disialyl structures by transfer of a sialyl group onto the GalNAc or GlcNAc residue inside backbone core chains having a terminal sialic acid with an alpha-2,3-linkage on Gal. ST6GalNAcVI prefers glycolipids to glycoproteins, predominantly catalyzing the biosynthesis of ganglioside GD1alpha from GM1b (PubMed:12668675, PubMed:17123352). Besides GMb1, MSGG and other glycolipids, it shows activity towards sialyl Lc4Cer generating disialyl Lc4Cer, which can lead to the synthesis of disialyl Lewis a (Le(a)), suggested to be a cancer-associated antigen (PubMed:12668675). Also has activity toward GD1a and GT1b, and can generate DSGG (disialylgalactosylgloboside) from MSGG (monosialylgalactosylgloboside) (By similarity).