Since I've seen many questions on the conjugation, here is the conjugation of the verb "manger" to the "présent de l'indicatif" :
- I eat = Je mange
- You eat = Tu manges
- He/She/It eats = Il/Elle/On mange
- We eat = Nous mangeons
- You eat = Vous mangez
- They eat = Ils/Elles mangent
For more information: http://french.about.com/od/verb_conjugations/a/manger.htm
If you have questions which are not answered in this comment or in the link provided, feel free to ask. Questions already answered will be deleted.
Thanks for your understanding.
"eux" is the disjonctive form of "ils", it could work in this exercise but is kind of tricky to accept as the disjonctive form isn't really learned at this stage of the course (also, just "Eux mangent." as a sentence, even though it's correct French, would be very rare and seem weird if used alone).
Something more commonly used with "eux mangent" could be something like: "Eh bien eux mangent. au moins." ("Well at least they eat.").