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The quoted passage is completely comprehensible; it's clear that the question is being asked by the character. The alternative would be absurd - the narrator making some kind of parenthetical comme...
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#4: Attribution notice removed
Source: https://writers.stackexchange.com/a/17153 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#3: Attribution notice added
Source: https://writers.stackexchange.com/a/17153 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
The quoted passage is completely comprehensible; it's clear that the question is being asked by the character. The alternative would be absurd - the narrator making some kind of parenthetical commentary on her own narrative! Adult readers of serious fiction will not be even momentarily confused by your example. The technique you're using is called 'free indirect style', and has been around for a long time, although it came to occur much more frequently in the heyday of the great realist novelists: Austen, Eliot, Tolstoy, Flaubert. It is not at all old-fashioned, however. It's very commonly used today by contemporary fiction writers. The habit of italicising characters' thoughts should be left where it belongs, in the pre-New Wave history of science fiction, and cheap pulp fiction thrillers. Unless you are writing 'young adult' or juvenile fiction, I would strongly advise you to continue to avoid italics, punctuation or any other clunky markers to separate chracters' thoughts from the enclosing narrative.