Catalyzes the addition of fucose in alpha 1-6 linkage to the first GlcNAc residue, next to the peptide chains in N-glycans (PubMed:15604090). The addition is prevented if the GlcNAc residue is already fucosylated (PubMed:15604090). Involved in susceptibility to the nematotoxic C.cinerea galectin Cgl2, likely by contributing to the synthesis of core alpha-1,6-fucosylated N-glycans to which Cgl2 binds (PubMed:20062796). GDP-beta-L-fucose + N(4)-{beta-D-GlcNAc-(1->2)-alpha-D-Man-(1->3)-[beta-D-GlcNAc-(1->2)-alpha-D-Man-(1->6)]-beta-D-Man-(1->4)-beta-D-GlcNAc-(1->4)-beta-D-GlcNAc}-L-asparaginyl-[protein] = GDP + H(+) + N(4)-{beta-D-GlcNAc-(1->2)-alpha-D-Man-(1->3)-[beta-D-GlcNAc-(1->2)-alpha-D-Man-(1->6)]-beta-D-Man-(1->4)-beta-D-GlcNAcl-(1->4)-[alpha-L-Fuc-(1->6)]-beta-D-GlcNAc}-L-asparaginyl-[protein] May also use Ca(2+). The enzyme has substantial activity without divalent cations. Inhibited by Fe(3+), Ni(2+) and Cu(2+). Optimum pH is 6-7.5. Protein modification; protein glycosylation. Membrane-bound form in trans cisternae of Golgi. Belongs to the glycosyltransferase 23 family.