a beta-D-galactosyl-(1->4)-N-acetyl-beta-D-glucosaminyl derivative + UDP-N-acetyl-alpha-D-glucosamine = an N-acetyl-beta-D-glucosaminyl-(1->6)-beta-D-galactosyl-(1->4)-N-acetyl-beta-D-glucosaminyl derivative + UDP + H(+) — reaction