I want to talk about some recent study on wall-crossing feature in D0-D2-D6 system via free fermion method. In the string theory side when we calculate the partition function for BPS bound states of D0-D2-D6 system. We can find out there are walls of the moduli space where BPS index can jump. While in the geometrical side it corresponds to the jump of Donaldson-Thomas invariants. I will talk about the counting procedure via the chain of dualities from D5-NS5 system to toric diagrams and to quiver and dimer and finally to crystal diagram. In some simple cases, the counting is related to some 3d Young diagrams or its generalization -- the crystal. And the idea is to slice those 3d Young diagrams to get a bunch of 2d Young diagrams and using the natural correspondence between 2d Young diagram and free fermion to build up the operator formalism in calculating the partition function for each chamber. If I have time, I will talk about the refined or motivic case of the wall-crossing feature.