Many commentators, e.g. Jerome, Bede, Ewald, Bertheau, and Hitzig, suppose that the father's instruction closes in the preceding verse, but it seems more appropriate to consider the father as here passing to another branch of his instruction, which is to point out the way of wisdom, and so to prepare for his warnings which follow from Proverbs 4:14 to Proverbs 4:19.
Receive; kakh, from lakah, "to receive" (on the force of this verb, see Proverbs 1:3). He who shows a delighter willingness in admitting the words of Wisdom—for such a character the father claims for his teaching, as we see from, the next verse—shall receive a blessing.
It is a sign of grace when any even show themselves open to listen to instruction; but it is a greater sign when this instruction is received with readiness and pleasure (Muffet). The years of thy life (sh'noth khayyim); literally, years of thy lives.
The plural "lives" expresses the idea of life in the abstract. There is no absolute statement of a future life here, though by the Christian this idea may be indulged in on the ground of a fuller revelation.
The promise is one that not only implies the prolongation of life, but also a life of prosperity and enjoyment. Shall be many; literally, shall be multiplied.