Solution: let the first chasing time be x and the second chasing time be y.

(1) Yang Yang caught up with Ningning for the first time, that is, the "ring". Yang Yang ran one more lap than Ningning, that is, Yang Yang ran 300 meters more than Ningning.

Then 6X=4X+300.

X= 150 second

Yang 6 *150 = 900m.

Ningning ran 4* 150=600 meters.

(2) When Yang Yang caught up with Ningning for the second time, Yang Yang ran twice more than Ningning, that is, 600 meters more.

Then 6Y=4Y+600.

Y=300 seconds

Yang 6 * 300 =1800m.

Because one lap is 300 meters, the remainder of 1800/300=6 lap is 0, which means that Yang Yang caught up with Ningning for the second time just at the starting line.

(3) Yang 6*300/300=6 laps.

Ningning ran 4*300/300=4 laps.