इमं विवस्वते योगं प्रोक्तवानहमव्ययम्।विवस्वान् मनवे प्राह मनुरिक्ष्वाकवेऽब्रवीत्॥
imaṃ vivasvate yogaṃ proktavān aham avyayamvivasvān manave prāha manur ikṣvākave ’bravīt
Word by word
The verse says
Krishna said: I taught this unfading practice to the sun. The sun told Manu. Manu told Ikshvaku.
In plain words
A new chapter, and it opens by handing you a chain of names.
Krishna taught the sun. The sun taught the first man. The first man taught the first king.
What Arjuna has been hearing for two chapters turns out not to be new. It is being returned to circulation.
Where you've felt this · in study
Your grandmother soaked rice a particular way before cooking it, and she learned that from her mother-in-law, who learned it from someone nobody can name now. You do it without thinking about it. The habit is older than every single person who has ever used it.
Going deeper
A thing that survives being handed down for that long is being claimed to survive the handing itself.
Avyayam - unfading, not wearing out. It is the same root as the akṣara at 3.15. What is transmitted does not degrade on the way, which is a strong claim about the thing rather than a compliment to the teachers.
And notice who receives it first: the sun. Not a sage. The chain starts outside the human world and comes down into it - sun, then the first man, then the first king. Knowledge arriving from above and entering history at exactly the point where somebody has to govern.
That descent matters, because avatāra is about to be defined. The pattern of something higher coming down into the ordinary is stated about a teaching before it is ever stated about a person.
The effect on a reader is to move the ground. Chapter 3 ended inside one person's head. This opens onto a span of time in which your own difficulty is very small and very old.