"They meet the man."
Translation:Ili renkontas la viron.
Transitive verbs take objects while intransitive ones are on their own. For example, in English, you can say:
"He closes the door (Li malfermas la pordon)" and "The door closes (La pordo malfermiĝas)"
The first one is in the transitive form since the subject exerts an action on an object (in this case, on the door) but the second one is in the intransitive form since it makes sense without the object, hence the -iĝ suffix.
For renkontas vs renkontiĝas, the same is true.
"They meet" = "Ili renkontiĝas" (Intransitive since there's no direct object) "They meet the man" = "Ili renkontas la viron" (Transitive since there's a direct object)
After reading the tips and notes, I thought both "Ili renkontas la viron" and "li viron renkontas ili" were correct, because I understood there was no particular order in Esperanto, since the object of the sentence is indicated by adding -n at the end of it; am I wrong? Or is it because it's "li viron" and not "la viron"? In that case, would "la viron renkontas ili" be correct aswell?
You are correct that Esperanto allows for a flexible word order, and the object is indicated with -n. However "li viron" is incorrect because "li" (Eo) translates as "he" (En), and "he man" wouldn't make sense. "la" (Eo) is the article for "the" (En), so "la viron renkontas ili" should be correct as well. Just keep in mind that the course is based on learning Esperanto from English, and by default the word order seems to typically follow English convention, whereas the answers with alternative word orders may or may not have been added by contributors as technically 'acceptable' answers.