Translation:This Friday I will see my mother, but not my father.
DL's dropdown for "vere" (with the tilde on the second e) here says it can be a form of the Spanish words for see, try and hear. It means "I will see" in this example; what are the infinitives for the Spanish verbs meaning "to try" and "to hear" that "vere" is also a conjugation for?
It might refer to the fact that we sometimes use the verb "ver" for things other than to see, I'll make it clearer.
Juan: ¿Vas mañana para la fiesta?
Ana: No sé si pueda, pero voy a ver.
There Ana used "ver" to mean that she will try look for a way to go to the party.
Juan: Oye! ¿Escuchaste la nueva canción de Demi? Está super.
Ana: No, aún no la he escuchado, a ver.
There Ana used ver to basically ask or tell Juan to let her listen to it. That may be the reason why Duolingo gave you those meanings in the drop down list. If you analyze it the same thing happens sometimes in English.