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The phrase 干你娘 is formed by combining the verb (gàn), which in vulgar slang means "to fuck", with the object 你娘, composed of the pronoun (nǐ) meaning "you" and (niáng) meaning "mother", resulting in a literal meaning of "fuck your mother".

Word Definition - 干你娘

gàn nǐ niáng (Tw) (vulgar) fuck you! (literally, "fuck your mother")