Hello, Olivia! Thank you for doing your homework for today. Here are your corrections...

    *********CORRECTED DIARY OF OLIVIA PARK**********

My best friend is Che Won. When I first met her, I wasn't friends with her. But as days past, we became friends. And, that's how I became friends with her.

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OLIVIA: my best friend is che won.
CORRECT: My best friend is Che Won.

EXPLANATION:

a. Don't forget to capitalize the first letter of any sentence.

b. Capitalize the First letter of a specific name.
____________

OLIVIA: when I first met her, I wasn't friends with her.
CORRECT:  When I first met her, I wasn't friends with her.

EXPLANATION:

a. Again, always remember to capitalize the first letter of any sentence.
____________

OLIVIA: But as days past,we became friends with each other.
CORRECT: But as days past, we became friends.

EXPLANATION:

a. Clear, short sentences are preferable, and more effective, than long, complex ones.
____________

OLIVIA: And thats how I became friends with her.
CORRECT: And, that's how I became friends with her.

EXPLANATION:

a. After the introductory conjunction, put a comma <,>

b. That's is a contracted form of "that is".
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So that's it, Olivia! Please study about these so that you will not commit the same mistake next time. Keep up the good work!