What is the correct Korean phrase for expressing gratitude?

The phrase "Gamsa Hapnida" is the appropriate way to express gratitude in Korean. This phrase directly translates to "Thank you" and is commonly used in both formal and polite contexts. Understanding the nuances of language is essential, especially when it comes to expressing gratitude respectfully.

The other options contain terms that either do not pertain to gratitude or are used in different contexts. For example, "Annyung Haship Nikka" translates to a greeting or asking about well-being, not gratitude. "Kook Ki Eh Dehayo Kyung Rye" might relate to a different concept altogether, and "Kwan Chang Nim Kae Dehayo Krung Rye" involves more complex formalities that are not specifically about thanking someone. Therefore, the simplicity and directness of "Gamsa Hapnida" make it the clear choice for expressing thankfulness in Korean.