Reducing geometry on a model is not just something to match a global polygon count, but more often, can be dynamically reducing areas where there less detail is necessary.

The trick is then to ensure that you are using quads while reducing to maintain some sort of polygon cohesion. Here Shane Benson, continues his look at SubDivision modeling in Cinema 4D with a look at some techniques for reducing the number of faces, while still maintaining quads for the model.

This lesson goes over one method to reduce highly subdivided meshes, to a lower subdivision count, while maintaining quads

Keeping everything as a quad is, at times overrated. Although there are definitely some times times when quads in a model are absolutely crucial. Typically and quite often, modeling with the intent of subdividing, in most applications will create quads in the end serendipitously, so it is just a matter of understanding how the edge flow will work between triangles and quadrangles with a bit of stratagem.