परित्राणाय साधूनां विनाशाय च दुष्कृताम्।धर्मसंस्थापनार्थाय संभवामि युगे युगे॥
paritrāṇāya sādhūnāṃ vināśāya ca duṣkṛtāmdharma-sansthāpanārthāya sambhavāmi yuge yuge
Word by word
The verse says
To protect those who are good, to undo those doing harm, to set right what is right — I come into being, age after age.
In plain words
The promise of 4.7 given its purpose. Three reasons, and the third is the one that holds.
Protect the good. Undo the harm-doers. And dharma-saṁsthāpanārthāya — for the sake of re-establishing what is right.
And then the phrase that keeps the promise open: yuge yuge — age after age.
Where you've felt this · in community
A neighbourhood association that lapsed twice and was restarted twice, by different people both times. It is not the same organisation. It is the same thing happening again.
Going deeper
The three purposes are not equal and the ordering rewards attention.
Protection and destruction are both instrumental. The third — dharma-saṁsthāpana, setting right what is right — is the actual aim, and the other two are how it gets done.
That matters for how vināśāya ca duṣkṛtām should be read. The destruction of wrongdoers is not presented as punishment. It is presented as clearing, in service of restoration. The distinction is thin and it is real, and traditions have used this line in both directions.
Yuge yuge — age after age — repeats the doubling of yadā yadā in the verse before. The Gita is describing a rhythm, not a single decisive intervention, and it declines to say this is the last one.
Which leaves a reader in a particular position. On this account there is no final settlement of things, and also no age in which nothing is coming. Both halves are load-bearing, and it is the second that the tradition has mostly carried.