We have a book of 360 pages.
He had already read 2/3 of the book, so there is 1-(2/3)=1/3 of the book left.
[tex]1-\frac{2}{3}=\frac{3}{3}-\frac{2}{3}=\frac{1}{3}[/tex]This means that 120 pages are left.
[tex]360\cdot\frac{1}{3}=\frac{360}{3}=120[/tex]If he wants to read the rest of the book in 4 nights, he has to read 30 pages a night.
[tex]\frac{120}{4}=30[/tex]