The answer shown above is grammatically correct, but it does sound odd in what I'd call everyday English. And so... "How many people are the letters from?" and "How many people are those letters from?" are also accepted. Your suggested alternative is not a translation of the Czech sentence in this exercise.
To my AmE ear, "Those letters are from how many people?" suggests an element of surprise -- as if, for example someone has a huge pile of letters that, it turns out, where written by only two people. So I can see it as acceptable on the English side, but I would leave it to the CZ natives on the team to decide if it's true enough to the Czech sentence to be added.
When using the selection option, the answer that is given by the choices is extremely weird for English. I dare say, it doesn't even make sense. Maybe if you add a comma between people and are, it might be easier to understand. But, as it is, if you said that sentence to me, I wouldn't understand it. The 'from' needs to come at the end of the sentence. The one caveat is if you speak Yoda. I would recommend changing the option when selecting the words to something like, how many people are those letter from. Another possibility, and maybe easier sounding would be, those letters are from how many people.
I was extremelly surprised with the proposed translation. The majority of textbooks would tell that 'from' as a first word in questionative sentences should be avoided. 'How many people are those letters from?' should be treated as acceptable and even more literally correct form
Is it just me......or is it annoying to other people that Duolingo always comes up with an error when we enter "these" but the answer is "those"? Or vice versa. In English I don't think there's a really massive distinction between "these" and "those", a difference yes, but you'd still be understood ok. Maybe it would be better if Duolingo came up with a suggestion of how to improve the answer, rather than a full error and to make us do the whole sentence again. Similarly, there's the same issue when using "this" and "that" on Duolingo. Any thoughts?
The course is quite consistent (with occasional exceptions) in its translations for "this/these" and "that/those." For the "basic" demonstratives -- ten/ta/to...-- the translation will almost always be "that/those." But when -to or -hle appears at the end of one of the basic forms, the translation will be "this/these." This is true for Czech-to-English and English-to-Czech.
Can this be annoying until we understand what's going on? Sure! But if there were no meaningful difference between the words, it is unlikely that either language would have both "this/these" and "that/those" equivalents.