For this case, we must fill in the blank with a verb that indicates the action taken by the subjects.
When speaking of letters, then the verb to use is to write. (Escribir).
We conjugate the verb in the present indicative we have:
Ellos escriben
(they write)
So, we have:
Carlos and Sofia write a letter to their family.
Carlos y Sofia escriben una carta a su familia.
Answer:
Escriben