Coyotes eat proteins in food. the proteins break down due to enzymes produced in the stomach of the coyote. the production of these enzymes then causes more enzymes to be released in the stomach. which process does this describe?

The production of these enzymes is called digestion.

Digestion the the process of breaking down the food (or in your case, protein) to smaller water-soluble food molecules so that they can be absorbed into watery blood plasma. This is necessary to distribute nutrients throughout the body.