"He cooks in the kitchen."
Translation:Él cocina en la cocina.
Aha! I see the confusion now! We're talking about different words. Everyone else is using the verb 'cocinar', which is, in my experience, the more usual word used. Cocinar is a regular 'er' verb. This is interesting - it's a word I've needed to use quite frequently in real life, and I don't think I've ever heard anyone use the irregular verb. I think we possibly need a native Spanish speaker to solve this, and explain why your answer isn't recognized.
OK, checked with a Spanish-speaking friend. Cocinar is the 'bucket' term which means 'to cook', in the same general sense as the English verb. Cocer means, specifically, to boil something in water. Apparently you wouldn't say 'hervir' in reference to boiling food (to boil an egg) - you would use 'cocer'. Hervir is specifically boiling a liquid, not boiling something in a liquid. This is probably why I was unfamiliar with the word - you can use 'cocinar' correctly to signify cooking any food, without getting more specific - but 'cocer' belongs to the more specific vocabulary set - in English, words such as fry, boil, grill, sauté, roast, simmer - they're all cooking. I learned something useful there!