This paper is a brief review of our previous relevant papers, it is narrated mainly from points of view of the predictions and the synthetic routes of the 120th and the 126th elements. Firstly we review the theories we constructed previously including the four principles of the theory of chirality, the chirality model of atomic nucleus and the periodic table of nuclides, the new circular periodic table of elements and the integrated periodic table of elements, the formulas of the fine structure constant and the formulas of the speed of light in atomic units as well as the formulas of the anomalous magnetic moments of electron, muon and tauon, then we mainly give the predictions and the synthetic routes of the 120th and the 126th elements including some new synthetic routes. Specifically, we regard that the 120th element has neutron number of 180 and the total nucleon number of 300 and the 126th element has neutron number of 188 and the total nucleon number of 314, regard they are relatively stable and most worthwhile and likely to be synthesized, and the 126th element is more important.