Catalysis of the reaction: N-acetyl-beta-D-glucosaminyl-1,6-beta-D-(N-acetyl-B-glucosaminyl-1,2)-beta-D-mannosyl-R + UDP-N-acetyl-D-glucosamine = N-acetyl-beta-D-glucosaminyl-1,6-beta-D-(N-acetyl-D-glucosaminyl-1,2-beta)-(N-acetyl-D-glucosaminyl-1,4-beta)-D-mannosyl-R + UDP.
uridine diphosphoacetylglucosamine-glycopeptide beta-1->4-acetylglucosaminyltransferase VI activity