Translation:The family is eating dinner.
Is there a difference between familie and gezin?
Familie includes your immediate family (parents, siblings) as well as your relatives (uncles, aunts, grandparents, cousins, etc). Gezin is like the English family, and usually just includes the parents and children.
"The family is having dinne." is also correct and should not be marked "wrong".
It would have been correct and accepted if you spelled dinner.