There seems to be a phrase or idiom associated with "learn this from that" in the Zen and Chan traditions of Buddhism.
The best way to start narrowing down philosophical phrases and their origins is to use major search engines for instances of usage. Very famous philosophical phrases such as cogito ergo sum may even have their own entries in tertiary resources like WP. In the case of "learn this from that", a quick examination seems to support Conifold's claim:
Project Gutenberg, Tao Te Ching Search "learn this from that" reports no instances of the phrase in their translation.
Google Search: "learn this from that" doesn't seem to indicate any consistent usage that might suggest inspiration from a philosophical work.
Google Books Search: "learn this from that" does seem to turn up many links to a theological work The Pilgrim's Progress, but
SEP Search: "learn this from that" has a link that suggests something related to Chinese philosophy, but the period in the results dismisses the possibility.
IEP Search: "learn this from that" doesn't return any results at all.
Lastly, of course, your memory may be inaccurate, and perhaps there is a phrase that resembles what you have represented here that is used that might be found. Or it's even possible that some translation of the Tao Te Ching (which wasn't written in English) did use that exact phrase but is obscure and uncataloged. But on the whole, baring additional evidence, I would say it's unlikely that "learn this from that" per se is associated with the Tao Te Ching.
But if we expand our search to using the keyword Zen (always my first go-to) which is associated with the Eastern religion of Buddhism, we seem to have some success.
Google Search: Zen, "this from that" reveals the idea of discrimination of things in the phrase "separate this from that", "discriminate this from that", and "discrimination and the division of 'this' from 'that'". In fact, this notion of binary division, if you have any familiarity with Zen, is a central tenet of examining how language creates artificial divisions experienced in reality.
From one of the links on the list Zen and Zen Classics: Mumonkan, p.68:
Daibai Obaku Isan Kyozan Kyogen Dramatis Persona Kyōgen ( Hsiangyen ), eleventh in the line of Zen after Daruma ... Before you came out of your mother's womb, before you knew this from that, your real self - speak, tell me what it is...
So, the phrase "before you knew this from that" given my understanding of Zen seems to allude to the same idea captured by Gilbert Ryle and others when talking about 'knowledge-how (ability to do) and 'knowledge-that' (ability to know). Children can drink milk long before they can explain they can drink milk.
Variation on discrimination, knowledge, recognition, and separation all of which resemble "LEARN this from that" seem to occur. Thus, while obviously since the phrase is English, this sense seems to have many synonymies used in the translation of Eastern philosophical thought.
What exactly, though, is the import of these synonyms? Simply put, it's is to raise awareness to point to the nature of the mind. Of course, Zen is famous for its koans which raise linguistic challenges to forge a path to satori.
In the contemporary Western analytical circles, for instance, it is known that bivalent logic and the Law of the Excluded Middle are biases of the mind, and not absolute truths about how to carve up reality with language, as graded membership is often a much more accurate way to model experience with language. In fact, there are an explosive number of non-classical logics that have a different take on how best to separate "this from that", and much confusion can arise even from bivalence and mutual exclusion.
Now, can we narrow it down? While I know almost nothing of the Eastern philosophical tradition, I suspect that given the fact that it is a translation, I would presume it's unlikely, though if it's important to you, if you start digging around in the Zen and Chan traditions of Buddhism, you might be surprised.
(Also, be careful of any expert who claims to know the world's philosophical tradition so well they can claim with certainty that any phrase is NOT a special phrase. Attempting to prove a negative is notorious in philosophical circles. There's just far too much for any one person to know, and is often a sign of overconfidence indicative of the Dunning-Kruger effect.)