day 1 = he reads 5/9 of the book
day 2 = he reads 7/18 of the book (see note below)
5/9+7/18 = 10/18+7/18 = 17/18 = 0.94 = 94% of the book is read in 2 days, so Neil does not finish the book in two days.
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note: 5/9 - 1/6 = 10/18 - 3/18 = 7/18