Catalyzes the hydrolysis of the 4-position phosphate of phosphatidylinositol 3,4-bisphosphate, inositol 1,3,4-trisphosphate and inositol 3,4-trisphosphate (PubMed:24070612, PubMed:24591580). Plays a role in the late stages of macropinocytosis by dephosphorylating phosphatidylinositol 3,4-bisphosphate in membrane ruffles (PubMed:24591580). The lipid phosphatase activity is critical for tumor suppressor function. Antagonizes the PI3K-AKT/PKB signaling pathway by dephosphorylating phosphoinositides and thereby modulating cell cycle progression and cell survival (PubMed:19647222, PubMed:24070612). {ECO:0000269|PubMed:19647222, ECO:0000269|PubMed:24070612, ECO:0000269|PubMed:24591580}. This is the function of INPP4B (inositol polyphosphate-4-phosphatase type II B, Ensembl gene identifier ENSG00000109452).