This trick is a combination of three around the world moves, two small & one big, one in one direction & two in the other. The trick is so called because the first two circles carry the diabolo around the string. More accurately though you move the string around the diabolo.
Get the diabolo spinning then swing it as if to do an Sun with a stop over (either side will do) so that the string loops around one handstick. However, instead of catching the diabolo on the string after it swings over the handstick pull your trailing handstick (the one the diabolo is swinging away from) back so that the diabolo swings down in front of the string & simply hangs in a loop suspended from the other handstick. Push the trailing handstick forward again & swing the diabolo up between your body & the string then over the handstick. As the diabolo passes over the stick point it downwards so that as the diabolo falls it pulls the loop off the end of the handstick. This brings you back to the starting position with the string crossed twice. Continue the diabolo's swing in the same direction into another Sun in front of the body to bring the diabolo back to the starting position with the string uncrosssed.
If your diabolo is spinning fast enough this move can be performed on both sides one after the other. Also try the whole move backwards.