Generally, one-syllable stems get the -at/et ending, and polysyllabic stems get the -tat/tet endings. Well, there are some other rules, when the verbs ends with "t", like "fut" and "futtat". If there is a consonant prior to the ending "t" you have to use "at/et", in the other case the "tat/tet" is the correct.

köszönöm szépen a magyarázatot! Just one think I still do not understand, when do I put tat/tet like sétáltatja and when -át,-et like vágat ( I mean why it is not vágtat or sétálatja?)? Also why there is diákokat - accusative (A tanár olvastatja a diákokat? vs diákokkal - with students (A tanár elolvastatja a leckét a diákokkal)?

Hey Edyta! These senteces all mean that someone is making other people do something for example: Ibolya is making his dog walk ( this is the literal translation for taking a dog for a walk), Éva is making Klári cut her hair, the teacher is making the students read, and the teacher is making the student read the homework. So if you put -tat/-tet after a verb it means someone makes somebody do something. -Tat or -tet depends on the vowels in verb: if there's e/é/i/í/ü/ű it's -tet, with other vowels ( or both categories) it's -tat. Have a nice day!