Questions & Answers about Η προθεσμία λήγει αύριο.
Η is the definite article in the feminine nominative singular (English the).
It matches the noun προθεσμία (feminine), which is the subject of the sentence. It’s capitalized (Η) only because it’s the first word of the sentence.
προθεσμία is feminine. A common clue is the ending -ία, which often (not always) forms feminine nouns in Greek.
Because it’s the subject here, it appears in the nominative singular.
It’s nominative because it’s the subject of the verb (λήγει).
Greek marks grammatical roles with case endings more than English does, so the noun form helps signal who/what is doing the verb.