A boy and girl can only form a line.

We need at least 3 to make a circle.

If we have 3, then we have ABC, ACB as arrangements,

as we can keep A still and move the other two,

but as far a making a circle is concerned it is always the circle ABC.

This is the view your book is taking.

For 4 girls and 4 boys...

If we fix one girl in place at the beginning of the line, there are

straight line arrangements of the remaining girls and boys alternating.

If they are arranged in a circle, that number is halved.