Correct option is D. Mr. Beebe asks the question in lines 6-7 ("Does . . .
quietly") primarily in order to note an apparent inconsistency.
Mr. Beebe sounds cynical (though he says he is not) of the fact that Lucy Honeychurch is someone who plays the piano beautifully and likes to live quietly. He believes that one these both qualities will 'mingle'. In the given context, it seems like Beebe believes that a person can not be both: good at music and like to live quietly. He thinks that it is reflects an inconsistency in Lucy's personality. Thus D is the best answer.
The lines of passage were -
Does it seem reasonable that she should play piano so wonderfully, and live so quietly? I suspect that someday she shall be wonderful in both. The water-tight compartments in her will break down,
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