Politely decline on the grounds of not being able to hold your liquor.
Tips
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A polite, somewhat formal way to turn down drinks at a Chinese business or family dinner, where outright refusal would be awkward. 胜 here is shèng = 'to be able to bear', as in 不胜感激 ('overwhelmed with gratitude').
mistakes
胜 is shèng here, not shēng. Don't confuse 不胜酒力 (can't handle drink) with 不省人事 (passed out cold).
