Answer:
The option that fills the blank is:
- <u><em>¿Cuál es la fecha de su nacimiento?</em></u>
<em>- Paula: </em><em>¿Cómo se llama? </em>
<em>- Sr. Fernando: </em><em>Me llamo Carlos Fernando. </em>
<em>- Paula: </em><u><em>¿Cuál es la fecha de su nacimiento?</em></u>
<em>- Sr. Fernando: </em><em>La fecha de mi nacimiento es el veinte de abril.</em>
Explanation:
The translation of the conversation is:
- Paula: What's his name?
- Mr. Fernando: My name is Carlos Fernando.
- Paula: What is your date of birth?
- Mr. Fernando: The date of my birth is April 20th.
The word <u><em>"cuál"</em></u> is an interrogative pronoun used to select a single option from a group of predefined options, in the case of a birth date, the predefined options are 365 days of a normal year (or 366 of a leap year) in which there may have been born a person, Mr. Fernando in this case, of which the correct option was April 20. Another way in which you could ask was:
- <em>¿Cuándo nació usted?</em>
But to use this form of a question you should not include the word <em>"fecha"</em>.