The sentence Elle mange ___ pomme chaque matin means "She eats ___ apple every morning." The blank requires a determiner before pomme, which is a feminine singular noun.
The correct answer is une (a/one), the feminine singular indefinite article. The sentence describes a habitual action: she eats one apple each morning. Une matches the gender (feminine) and number (singular) of pomme.
The other options are incorrect:
la (the) is the feminine singular definite article. While la pomme is grammatically valid, Elle mange la pomme chaque matin would mean she eats a specific, identified apple every morning, which is semantically odd for a daily habit
du is the masculine singular partitive article (used with uncountable nouns like du pain). Pomme is feminine and countable, so du does not agree
des is the plural indefinite article. Pomme is singular here (no -s), so des does not agree in number
The complete sentence is: Elle mange une pomme chaque matin - She eats an apple every morning.