Put it in the B configuration. There are 12 boys, which can be thought of as 24 halves bundled in pairs: a half on the outside of the circle, and a half on the inside of the circle. (Conveniently, also, each bundled pair of halves includes one half with a flag and one half without a flag). Some of these halves are more substantial looking than others, mind you.
Rotate it to the A configuration: There are still 24 halves, bundled in pairs. But now we count it as 13 boys instead of 12. Why? Because in the bottom left, two of the halves that got paired together are both flag-and-head halves, so even though that was just two halves in our original count, it feels like the two of them bundled together should count as two boys instead of just one now.
(Correspondingly, in the top right, two of the halves that get bundled together in the A configuration are both non-flag halves. But the result still seems sufficient to call one full boy instead of zero boys.)
Rotate it to the A configuration: There are still 24 halves, bundled in pairs. But now we count it as 13 boys instead of 12. Why? Because in the bottom left, two of the halves that got paired together are both flag-and-head halves, so even though that was just two halves in our original count, it feels like the two of them bundled together should count as two boys instead of just one now.
(Correspondingly, in the top right, two of the halves that get bundled together in the A configuration are both non-flag halves. But the result still seems sufficient to call one full boy instead of zero boys.)