Declensions are totally wrong:
Accusative feminine of мой is мою (see the table here: https://en.wiktionary.org/wiki/%D0%B...%D0%B9#Russian)
Accusative of жизнь is жизнь. (https://en.wiktionary.org/wiki/%D0%B...B7%D0%BD%D1%8C)
Dative of ты is тебе (https://en.wiktionary.org/wiki/%D1%82%D1%8B#Russian)
Good news! Dative of Грег is Грегу.
Bad news: you actually don't need dative here, since it is just a name of a person you are talking to.
More bad news: the whole sentence is terribly wrong.
The correct translation is "Я обязан тебе жизнью, Грег" (literally: I am obliged to you by my life)
God, why??? Why do you choose SUCH sentences to translate every time?
(sigh)
This is your homework on declension and pronouns:
Femenine nouns of Declension 1. Translate the sentences:
1. I have a dog.
2. My dog is very big.
3. I love my dog very much.
4. I see my dog.
5. My dog sees me.
6. I gave a piece of meat to my dog.
7. My sister has a cat.
8. The cat hates my dog.
9. My dog is afraid of this little beast.
10. The cat loves my sister only.
11. The cat is drinking water.
Vocabulary:
собака - a dog
кошка - a cat
сестра - a sister
маленькая бестия - a little beast
вода - water
Femenine nouns of Declension 3. Translate the sentences:
1. I see my mother.
2. The mother loves her daughter.
3. The daughter loves her mother.
4. I see a mouse.
5. I gave a piece of cheese to the mouse.
6. The mouse looks happy.
7. A horse eats rye.
Vocabulary:
мать - a mother
дочь - a daughter
мышь - a mouse
лошадь - a horse
рожь - rye