I am not able to reply to that thread; I think maybe threads with double quotes in the title mess up responses to the thread somehow. Anyway, jen my response.

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Basically, "da" is used only with amounts. If you have a noun or an adverb that represents an amount of something, use "da" to show what it is the amount of. This is easier to explain with some prototypical examples...

centoj da loĝantoj ("hundreds of residents")
Centoj here is a noun that indicates amount. Da is needed here because centoj, as a noun, cannot directly modify loĝantoj (which is obviously also a noun). Since you can't really change centoj into an adjective without significantly altering the meaning of the phrase, leave it as a noun and use da.

cent loĝantoj ("a hundred residents")
Da is not needed here even though cent is clearly an amount because the cardinal numbers (unu, du, tri, etc, including cent) when used without grammar endings are considered to be adjectives. Since an adjective can modify a noun directly it of course has no need for a preposition.

multe da mono ("a lot of money, much money")
Multe is an adverb showing amount. Since an adverb cannot directly modify a noun (in this case mono), you need da. It is also possible to construct mult- as an adjective (multa mono), but that type of construction (i.e. using multa in the "singular") seems rare for some reason. Multe da is the prefered construction for the equivalent of English "much" and multaj is prefered for "many".

multaj homoj ("many people")
Here, mult- is formed as an adjective (multaj) and so can modify homoj directly.

kiom da tasoj ("how many cups")
All of the -iom correlatives are considered adverbs. As such they need the help of da if you want them to modify a noun. (Of course technically kiom isn't really modifying tasoj here -- indeed it can't -- instead the whole prepositional phrase da tasoj modifies kiom, and kiom in turn is considered to modify something else in the sentence, the verb perhaps, but all of this is somewhat of a hair-splitting point).

kiom ili kostas? ("how much do they cost?")
Here, kiom modifies kostas -- a verb -- so da is not needed (an adverb of course can modify a verb directly).

kiom da eŭroj ili kostas? ("how many Euros do they cost?")
Here, kiom wants to modify (or perhaps more precisely, be modified by) a noun so use da.

kiom da ili vi aĉetos? ("how many of them will you buy?")
And here kiom wants to modify a pronoun (which is essentially a noun) and so it does need da. (Note ili is not accusative because it's the object of a preposition).

la ekzameno estis iom facila ("the exam was somewhat easy")
Here iom is an adverb indicating amount, but since it modifies an adjective facila, it doesn't need da, even though facila in turn modifies ekzameno (a noun).

la ekzameno enhavis iom da facilaj demandoj ("the exam contained some easy questions")
In this somewhat similar sentence, iom pertains to demandoj (not facilaj) and so da is needed. If you wanted iom to modify facilaj instead of demandoj (i.e., "somewhat easy questions" instead of "some easy questions"), you would reword it thus: la ekzameno enhavis iom facilajn demandojn. (Note that facilajn and demandojn are now accusative since they are no longer the objects of the preposition da, but are now direct objects).

mi parolas iom da la angla ("I speak some English")
Tricky eh? In Esperanto you are permitted to drop nouns if the words modifying them make it clear what you are talking about (or if the noun would merely be something essentially meaningless like "things" or "ones"). This is particularly common with languages, where la angla is understood to be short for la angla lingvo in most contexts. When you do this though, keep in mind that all the other words in the sentence have to act as if the "ghost noun" (that's what I call it; I don't know the technical term) is still there. In the above example sentence, iom wants to modify the ghost noun lingvo -- not the adjective angla -- but can't (due to the fact that iom is an adverb) so da is needed.

mi parolas ĝin iom ofte ("I speak it somewhat often")
Since an adverb can of course modify another adverb, iom can be put with ofte without any fuss.

Meanwhile "de" is used for most non-amount senses of the English "of"...except for those times when el or pri are indicated instead.