"We are reading a book to them."
Translation:Nous leur lisons un livre.
"les" is for direct objects; when you're reading a book to someone, the book is the direct object and the people you're reading it to are indirect objects.
It's not correct to use "à eux" here, it has to be "leur".
In fact, saying "nous lisons un livre à eux" would take a different meaning and mean "We are reading a book of theirs"
The English plural object pronoun is "them", which is object-neutral, like all English object pronouns.
To explain that a little better, consider the sentence: "We are reading a book to them." Here, "them" acts as an indirect object. The book is the direct object, because it's the thing that's actually being read. The verb "to read" acts on the book directly.
Now consider the sentence "We are reading them." Here, "them" is the direct object, the thing the verb acts on, the thing being read. In English, it's the same word, but French makes the distinction explicit. As piguy3 said, you use "les" for direct plural objects and "leur" for indirect ones.
"Those" is actually the English distal plural demonstrative (that is, the plural form of "that"). Grammatically, it can function as a pronoun in many of the same contexts as "them", but you wouldn't normally use it that way with reference to a group of people.
can we conclude that "lui" replaces à+singular while "leur" replaces à+plural ?
I think you've got the general idea right, but some problems arise with the specific phrasing. "lui" is for singular indirect objects (those to whom something is e.g. read or given); "leur" is for plural indirect objects.
Whether this precisely correlates to à + something is a different matter. See, among other potential issues, relox84's response to RedTyphoon.
I got "We are reading a book to them" and didn't get it quite right but the correct answer came up as "Nous leur avons lu un livre" - this seems to be incorrect! I have reported it.
nous leur lisons un livre is the correct translation for this sentence Duo's correction for this exercise is wrong. vous leur avons lu un livre... it is past tense. the sentence here is present tense. I have received the wrong correction because I made a word order mistake.