Answer: escribirán
This sentence written in future is related to a book Carlos and Sofía (they) will write before leaving Puerto Rico.
In this context, the correct conjugation of the verb escribir (to write) in future (indicative mood) with the 3rd person in plural ellos (they), is escribirán (they will write).
Therefore, the complete sentence is:
Antes de salir de Puerto Rico Carlos y Sofía escribirán un libro sobre la historia de Puerto Rico.
Carlos and Sofía will write a book about the history of Puerto Rico before leaving Puerto Rico.
