"Their pig eats rice."
Translation:Leur cochon mange du riz.
In English, the word some in the construct some of something may be dropped but in French it usually cannot be dropped.
Je mange du pain avec de la confiture. - I am eating bread with jam.
Il y a des fourmis partout. - There are ants everywhere.
des is either:
an idefinite article associated with plural countable nouns.
the contraction of the preposition de + the definitive article les
Therefore, des can mean some or of the or from the, etc.
Je vais manger des fraises. - I am going to eat (some) strawberries.
Il arrive des États-Unis. - He's coming from the United States.
Aimeriez-vous des pommes ? Would you like (some) apples ?
ce sont des soldats - they are soldiers
ce ne sont pas des amis. - they are not friends
Now here comes the tricky bit. In English you cannot always drop the word some in constructs some + noun
For example, consider the sentence Some people like marmite. In such a construct you cannot drop the word some because if you did it implies people in general like marmite which is definitely not the case.
Another example where the word some cannot be dropped is: Some days I don't feel at all well
When the word some means a certain proportion rather than an indefinite number then you use the french word certain(e)
Certains hommes sont mauvais. - Some men are bad.
Certains jours je ne me sens vraiment pas bien - some days I don't feel at all well
Voulez-vous certaines des pommes ? - Do you want some of the apples ?
It took me a while to understand this as well. In simple terms, 'rice' is an item of 'some' unknown quantity being consumed because they come in individual kernels of rice. So you wanna use 'du', because it doesn't state what amount the pig eats. "Their pig eats some rice" and "Their pig eats rice" is the same in French. If its "Their pig eats 'the' rice" then its a specified amount and refers to the whole rice available, which translates into "Leur cochon mange le riz". Its quite confusing and the best way to learn this is repetition in your studies until it becomes second hand nature.