Catalyzes the hydrolysis of the 4-position phosphate of phosphatidylinositol 3,4-bisphosphate (PtdIns(3,4)P2). Catalyzes also inositol 1,3,4-trisphosphate and inositol 1,4-bisphosphate. Antagonizes the PI3K-AKT/PKB signaling pathway by dephosphorylating phosphoinositides and thereby modulating cell cycle progression and cell survival. May protect neurons from excitotoxic cell death by regulating the synaptic localization of cell surface N-methyl-D-aspartate-type glutamate receptors (NMDARs) and NMDAR-mediated excitatory postsynaptic current.; Displays no 4-phosphatase activity for PtdIns(3,4)P2, Ins(3,4)P2, or Ins(1,3,4)P3.