1. Park your car on a flat, stable surface and apply the parking brake.
2. Loosen the lug nuts with a lug wrench, but do not remove them completely.
3. Use a car jack to lift the car off the ground. Make sure the jack is placed on a solid, non-moving part of the car's frame.
4. Remove the lug nuts and take off the flat tire.
5. Place the new tire on the lug bolts. Hand-tighten the lug nuts to hold the wheel in place.
6. Lower the car until it is almost touching the ground, but leave a small gap.
7. Use a lug wrench to tighten the lug nuts as much as possible while the car is still slightly lifted.
8. Lower the car all the way to the ground.
9. Retighten the lug nuts with the lug wrench, using all your strength to ensure they are as tight as possible.
10. Double-check that the lug nuts are tight.
By following these steps, you should be able to change the tire on your Mazda RX-8 and ensure that the lug nuts are fully tightened. Remember always to take necessary safety precautions when working with a car jack or changing tires.