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The phrase 干你娘 is formed by combining the verb 干 (gàn), which in vulgar slang means "to fuck", with the object 你娘, composed of the pronoun 你 (nǐ) meaning "you" and 娘 (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")