During the period of the Three Kingdoms in Korea, the spread of Chinese influence occurred through several means, but the most significant ways included:
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Through the introduction of Chinese art and technology: The Three Kingdoms of Korea (Goguryeo, Baekje, and Silla) adopted various aspects of Chinese culture, including art styles, metallurgy, and agricultural practices.
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Through the Chinese writing system: The adoption of Chinese characters (hanja) for writing also played a crucial role in the spread of Chinese influence, facilitating the transmission of literature, philosophy, and governance concepts.
While the travels of Chinese Buddhist monks contributed to the spread of Buddhism and Chinese influence, and military conquests also had an impact, the most defining mechanisms were the introduction of art, technology, and the writing system.
If you need the best single answer based on the options you provided, it would be through the Chinese writing system.