1) Let's make a graph for that round trip with stops.
2) Continuing the graph, on the way back
Considering that every time the plane stops, its altitude goes down to 0, i.e. a point in the x-axis, then we can count 4 stops, 1 in the Chicago-NY and 3 on the way back. Considering that the graph touches the x-axis when it lands then the graph touches 6 times