The sentence Elle prend __ café tous les jours ("She has __ coffee every day") requires a partitive article before café. In French, the partitive article is used to express an unspecified quantity of an uncountable noun ("some").
Since café is masculine singular, the correct partitive article is du (contraction of de + le). The complete sentence is: Elle prend du café tous les jours ("She has [some] coffee every day").
The partitive articles in French are:
du - before masculine singular nouns (du pain, du café)
de la - before feminine singular nouns (de la confiture)
de l' - before singular nouns starting with a vowel (de l'eau)
des - before plural nouns (des fruits)
The other options are incorrect: de alone is used in negative sentences (elle ne prend pas de café) or after expressions of quantity; d'un means "of a" and is not a partitive form; d'en is not a valid article combination in this context.
