A 20cm long rubber string obeys hookes law. When it is stretched by 4 cm ,its lowest resonant frequency is Vo. When it is further stretched by 2cm, find whether the new lowest resonant frequency is greater than or less than or equal to Vo.

Resonant frequency is independent of stretching. It only depends on mass and hooke’s constant

In that case you can assume that the string will follow the hooke’s law only for half of it’s path. When it reaches the mean position, it follows simple motion under gravity. Because it is thrown up with a lesser speed as compared to the first case, it will come back faster, hence the total time taken will decrease. That explains why frequency will be more.
Hope that answers your quesiton