In this paper, we examine directed self-assembly in a 2D binary system of dipolar and quadrupolar colloidal particles with normal surface boundary conditions, dispersed in the nematic liquid crystal. Using the laser tweezers, we assembled a large variety of stable 2D colloidal crystal structures. In all analyzed structures, the particles, their surface treatment and the cell conditions were the same, which gives us the ability to systematically follow the evolution of colloidal assembly when many particles are present. We present an analogy between molecular self-assembly and organization of colloidal microspheres in liquid crystalline medium to extend the strategy for designing colloidal crystalline structures of different level of complexity.