This is from a problem from my Chinese book; I'm practicing the use of 怎么 (zěn me).
Měiguó péngyǒu huì zuò zhōngguó cài, nǐ juédé hěn qíguài, wèn tā: ...
This translates to "An American friend can cook Chinese food; you feel it's strange. [You] ask him: ... " I came up with two answers:
The first I think is fine: 你怎么会做中国菜？ (Nǐ zěnme huì zuò zhōngguó cài?) meaning "How can you cook Chinese food?"
My second answer I'm uncertain about because of the repeated 怎么, and because it's an almost-direct translation from English:
Nǐ zěnme zhīdào zěnme zuò zhōngguó cài?
By this I intend to ask him "How do you know how to cook Chinese food?"
Question: Is 你怎么知道怎么做中国菜? a grammatically correct question?