Building on the last talk, we will continue to explore the connection between the completely packed loop models (CPL) and the six vertex model through the lens of the (affine) Temperly-Lieb algebra. We will introduce the Temperley-Lieb algebra as a quotient of the Hecke algebra and see how the Yang-Baxter equation shows up naturally in this setting. We will realize CPL and the six vertex model as representations of this algebra and use this representation to study the relationship between the two models.