After . . . . . . . . fourth lesson, English students have . . . . . . . . break of . . . . . . . . hour and . . . . . . . . half for dinner.

In the first blank, it is specifically mentioned that it is the "fourth lesson", hence, article "the" will be used.
In the second blank, article "a" will be used because the speaker is mentioning about something 'general'.
Similarly, In the third and fourth blank, article "an" and "a" will be used respectively because 'hour' has a vowel sound and 'half' has a consonant sound.