"His dog is alive."
Translation:Ο σκύλος του είναι ζωντανός.
Το σκυλί σου είναι ζωντανό, what is wrong with that? Childish, colloquial or whatever, but it is still correct, isn't it?
Here needs "του". It says "his dog". It's in the incubator. If you wrote του but was not accepted, I imagine you found it on a strengthen exercise.