Right answer:
escriben
Escriben is the conjugation of the verb escribir for the third person plural in the simple present. The simple present tense is used to talk about habitual actions and routines or to describe things that happen now or in the near future. So in this sentence this is used to describe that children are writing letters to their father, that is, this happens now. So los niños can be replaced by the subject pronoun that matches the third person plural, which is ellos. Finally:
Los niños escriben las cartas a papá