Hello can someone please try to explain this to me as simply as possible

The easiest way to solve this problem is to substract 2π from the angle until we get an angle that is less than 2π.
[tex]\frac{19}{3}\pi-2\pi=\frac{19-6}{3}\pi=\frac{13}{3}\pi[/tex]13/3π is not less than 2π, so we have to substract 2π once more:
[tex]\frac{13}{3}\pi-2\pi=\frac{13-6}{3}\pi=\frac{7}{3}\pi[/tex]7/3π is still not less than 2π, substract 2π once more:
[tex]\frac{7}{3}\pi-2\pi=\frac{7-6}{3}\pi=\frac{1}{3}\pi[/tex]1/3π is less than 2π. It means that the positive angle less than 2π that is coterminal with 19/3π is 1/3π.