a beta-D-galactosyl-(1->3)-N-acetyl-alpha-D-galactosaminyl derivative + UDP-N-acetyl-alpha-D-glucosamine = a beta-D-galactosyl-(1->3)-[N-acetyl-beta-D-glucosaminyl-(1->6)]-N-acetyl-alpha-D-galactosaminyl derivative + UDP + H(+) — reaction