When someone says "domo arigato" (the formal Japanese phrase for "thank you very much"), appropriate responses depend on the social context. In casual settings, you can reply with "douitashimashite" (you're welcome), or simply respond in English with "you're welcome," "no problem," or "glad to help." In a polite or business environment, acknowledging the courtesy with a warm smile, a nod, or an appreciative phrase maintains proper etiquette and mutual respect.