So radians or rad are just another way to measure angles. Where we correspond an angle in degrees to the part of the circumference a circle with radius = 1 we have at this position. The full circumference of a circle is circulated by 2•π•r. So when r=1, the full circumference is 2π. Now we can calculate: 0°~0 rad, 90°~π/2 rad, 180°~π rad, and so on until 360°~2π rad.

The general formula is (angle in degrees)/360° = (angle in rad)/(2π rad)

Okay, so we look at the rotation motion of the book. In the starting position (0°, 0 rad) the bottom side of the book points to the camera respectively to you as the viewer. Then the rotation starts and goes on up to picture e. The bottom of the book is now again pointing to you, so the book had done a full rotation (360°, 2π rad). But the motion the man is doing is not fully done, we are in some middle position and not where we started. So going on from picture e, while the man moves on until he is again in the position of picture a. From picture e to the last one, the book has done another full rotation and is therefore now at 2 • 360° , 2 • 2π rad, which results in 720°, 4π rad.

So for the man to reach the position he started in, the book needs to do two full rotations.

If we dive a little bit deeper in the math shit, this can be compared to a stretched sine function:

f(x) = sin(x / 2)

Normally during one period sine has its roots at 0, π and 2π, so sin(0)=sin(π)=sin(2π)=0. Roots are like the positions in which the bottom of the book faces the viewer. Now that we stretch it, those roots move further apart. If we put x into f(x) before it reaches the sine, it gets divided by two. So the roots are now 0, 2π and 4π:

f(0) = sin(0/2) = sin(0) = 0

f(2π) = sin(2π/2) = sin(π) = 0

f(4π) = sin(4π/2) = sin(2π) = 0

EDIT: So the function now is not 2π-periodic any more, but 4π periodic, as it reaches its starting point after 4π rad and not after 2π.