a beta-D-Gal-(1->4)-beta-D-GlcNAc-(1->3)-[beta-D-GlcNAc-(1->6)]-beta-D-Gal-(1->4)-N-acetyl-beta-D-GlcNAc derivative + UDP-alpha-D-galactose = a beta-D-Gal-(1->4)-beta-D-GlcNAc-(1->3)-[beta-D-Gal-(1->4)-beta-D-GlcNAc-(1->6)]-beta-D-Gal-(1->4)-N-acetyl-beta-D-GlcNAc derivative + UDP + H(+) — reaction