Hiroshi is at his wit's end. He's lost the only copy of the book he needs for his report.
Literal
Hiroshi [topic-は] troubled-exhausted [explanatory-のよ]. Report [object-を] write [for-のに] necessary one-copy only [possessive-の] book [object-を] lost-[regret-てしまったの].
困り果てている 'is completely at a loss' — 困る 'to be troubled' + 果てる 'to be exhausted/at the end of.' 一冊しかない本 'a book of which there is only one copy.' なくしてしまった 'ended up losing' — regrettable completion. The feminine のよ and の mark the speaker as female, narrating sympathetically.