an idiom meaning to be astonished, bewildered, or flustered — literally 'to make one's eyes go white and black' (showing confusion or surprise).
あまりの量に、店員は目を白黒させながら対応していた。
The clerk was flustered while dealing with such a large amount.
子どもたちはマジックのトリックを見て目を白黒させた。
The children were astonished and bewildered watching the magic trick.
教授の難しい説明に学生たちは目を白黒させていた。
The students were bewildered by the professor's difficult explanation.
想定外の質問に、彼女も思わず目を白黒させた。
She too was momentarily flustered by the unexpected question.