I take a vacation.
l get in to this game.
I need to look for the baby.
They cannot believe their eyes.

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1.
Alice: I take a vacation.
Correct: NO CORRECTION

2.
Alice: l get in to this game.
Correct: l get in to this game.
Explanation:
*Get in means enter. You cannot say "I enter to this game." It should be "I enter this game."

3.
Alice: I need to look for baby.
Correct: I need to look for the baby.
Explanation:
*Add an article before the noun baby.

4.
Alice: Not belive one's eyes oK?
Correct: They cannot believe their eyes.
Explanation:
*I just used the words in your sentence because I don't get the meaning of that. Not believe one's eyes means be very surprised to see something.
*Be careful with your spelling. (believe)

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Hello, Alice! Thank you for submitting your homework. Please read the following corrections and explanations carefully. If you have questions and clarifications, you can ask me in our class. Thank you!