"František, you do not age."
Translation:Františku, vy nestárnete.
It's possible with or without the pronoun - "Františku, (ty/vy) nestárneš/nestárnete."
This particular sentence is more common with the pronoun, with the meaning "YOU - as opposed to other people - don't age." So the pronoun is stressed.
Omitting the pronoun would be natural in a dialogue similar to this:
František: "Myslíte, že stárnu?"
Duo: "Františku, nestárnete!" (more like "you DON'T age")
Generally the correct answer for the sentence in the exercise appears among the hints. I just checked for this sentence, and Františku is actually the first one listed. Unfortunately, I can't tell you why you're not seeing it. However, it's good to keep in mind that often forms of a word that would be correct in a different sentence also appear in the hints for the exercise sentence.