The University of Houston main campus offers a very large number of degrees. There isn't a single, readily available number that encompasses *all* degrees (e.g., counting every specialization within a major as a separate degree). The university's website lists degrees by college, and then further by department, making a precise count difficult to obtain without manually compiling it from numerous pages.
To get an idea of the scale, you'd need to look at the many colleges within the university (e.g., College of Engineering, College of Liberal Arts and Social Sciences, etc.) and then examine the programs offered within each. You'll find hundreds of undergraduate and graduate degrees.