According to the excerpt how does Buddha say that one can escape the cycle of rebirth?

If liberation is achieved

Explanation:

One can escape the cycle of rebirth if liberation is achieved and this can be done by insight and putting out desires.

Samsara is cycle of existence, endless rebirth and Samsara is caused by karma which is one's actions resulted from an intentional mental or physical deeds which subsequently caused a future consequences. Liberation from Samsara is refer to as Nirvana

Nirvana which means "blown out" is a word associated to Buddhism, Hinduism and Jainism can be refer to as a state of being free soteriologically.