For this case we can translate the dialogue as:
_______you go to the restaurant?
The _____, after the game.
We must complete with the most appropriate option.
It is observed that the second sentence begins with a definite article, masculine in the singular.
So, the option that best fits is: El martes ...
"El mediodía" is not correct in Spanish. The correct form would be "Al mediodía"
On the other hand, as one speaks of time, then the first sentence should contain "Cuándo"(When), which is an adverb of time
So, we have:
—¿Cuándo vas al restaurante?
—El martes, después del partido.
Answer:
Option C