"The girl eats her food."
Translation:Pigen spiser sin mad.
The possessives sin/sit/sine always mean his/her own. To translate the sentence here, "The girl eats her food", if you mean that she eats her own food, that would be "Pigen spiser sin mad", as Duo says. But if you mean she eats another woman's food, the correct translation would be "Pigen spiser hendes mad."
"Hende" is the accusative form of "hun" and so is used as the object of the sentence. For example:
Jeg elsker hende. = I love her.
"Hendes" means "her(s)" and so is used when an object belongs to "her" except when "she" is mentioned already in the clause which I'll mention next. So:
Hendes hund. = Her dog.
"Sin/Sit/Sine" are used to mean "her" (but can also mean "his" and "its") when "she" is already mentioned in the clause. For example:
Hun elsker sin hund. = She loves her (own) dog.
If you were to use "hendes" instead of "sin" it means that she loves someone else's dog.