Specifically cleaves terminal alpha 1,6-linked mannose residues on Man3GlcNAc and Man2GlcNAc core oligosaccharides generated by N-glycan degradation pathways, having little activity, if any, on larger mannose oligosaccharides (PubMed:1577805, PubMed:16115860). Does not cleave terminal alpha 1,6-linked mannose on Man3GlcNAc2, and is also unable to hydrolyze terminal alpha 1,3-mannose linkages (PubMed:1577805, PubMed:16115860). {ECO:0000269|PubMed:1577805, ECO:0000269|PubMed:16115860}. This is the function of ENSG00000013288 (MAN2B2, mannosidase alpha class 2B member 2).