Catalysis of the hydrolysis of (1->6) linkages between alpha-L-fucose and N-acetyl-D-glucosamine in glycopeptides such as immunoglobulin G glycopeptide and fucosyl-asialo-agalacto-fetuin.
1,6-L-fucosyl-N-acetyl-D-glucosaminylglycopeptide fucohydrolase activity