How do I get my Cat to stop puking on my room’s white carpet?

You need to get him to the vet to find out if he’s having stomach issues. This will be cheaper and easier than constant carpet cleaning in the long run. Another option is closing the door to your room but don’t be angry with him, he’s not doing it to be bad. You can also try putting down a brown, fuzzy rug inside the room and praise him if he lands it there, for several weeks, then close the door and move the rug until it’s on the regular floor. Continue to praise and treat the good behavior and eventually maybe you’ll be tossing the rug outside the back door and he’ll choose a spot just inside. Time, consistency and patience are all it takes.