下厨 is a separable verb (离合词) meaning 'to go into the kitchen and cook' — it emphasizes the act of personally preparing a meal rather than just cooking in general. You can separate the two syllables, e.g., 下了一次厨 ('cooked once'), and the object of cooking is usually introduced with a different verb (做菜) rather than placed after 下厨. The word carries a slightly warm, domestic tone — it's what you say when you've cooked for someone or decided to cook yourself instead of eating out.