"Péter is reading the old book."
Translation:Péter a régi könyvet olvassa.
Very good question. The Hungarian sentence "A régi könyvet Péter olvassa" is not incorrect per se, but its word order relies on the assumption that in the English sentence the emphasis is on "Peter", whereas the English word order implicitly follows the principle of end focus, according to which in this sentence the expected focal item is "the old book".
In contrast, the word order in "A régi könyvet Péter olvassa" explicitly puts the emphasis on "Péter", assuming the meaning that it is Peter (rather than John) reading the old book. But the assumption of Peter being the focal unit is justified only if we are informed of the intonation of the English sentence, whereby "Peter" is uttered with emphasis.
Since Hungarian is an inflected language, its word order is not as rigid as that of English and of many other languages, but in many cases the different word orders in Hungarian express different emphasis, and in this regard there are semantic limits to the structural flexibility. There are rules establishing these limits, which will probably be explained in detail at a later stage of the Duo course.
The main points of the rule: to emphasise the verb, we put the verb at the start of the sentence; whereas in the case another sentence element is to be emphasised, it is put before the verb.