I think the answer is two times.
Sorry for the poor quality sketch. The contact point between the coins "travels" a distance of 6pi. The smaller coin has a circumference of 2pi. Therefore the smaller coin "rolls" three times during the trip. But point B only circumnavigates point A twice. It would circumnavigate three times if the trip had been in a straight line. But one doesn't happen because the distance traveled was a circle.
