Preheat the oven to 350°F and spray a 9x13-inch baking dish with cooking spray. Set aside.
In a large skillet over medium heat, cook the ground beef until no longer pink. Drain grease.
Add the onion and cook for 5 minutes, or until softened. Add minced garlic and continue to cook for an additional 2 minutes.
Add taco seasoning, red and green enchilada sauce, and diced green chiles. Stir well. Let simmer on low for 5 minutes.
Divide meat mixture into 8 equal portions. Fill each tortilla with an equal amount of meat mixture.
Divide 2 cups shredded Mexican blend cheese into 8 equal portions and place on top of each tortilla with the meat mixture. Roll the tortillas tightly.
Pour ⅓ of the 28-ounce can of enchilada sauce into the bottom of the 9x13-inch baking dish. Place rolled tortillas seam side down.
Pour the remaining enchilada sauce from the 28-ounce can on top of the flour tortillas. Top with the remaining 1-1½ cups of Mexican blend shredded cheddar cheese.
Place the baking dish in the oven and bake uncovered for 20 minutes.