In 2022, Junie T. Go gave a connection between the Terwilliger algebra of hypercube and the universal enveloping algebra U(sl2) of sl2. In this talk, I will give a brief introduction to the Q-polynomial distance-regular graphs and the Terwilliger algebras. Subsequently, I will present my recent work with my Ph.D. student Chia-Yi Wen on the even subalgebra of U(sl2) and its connection to the Terwilliger algebras of halved cubes.