Can anyone check my letter?

Nix the second line and change it to ” I was impressed with your enthusiastic attitude”

Drop the plural on ‘staffs’ to ‘staff’, and change ” I wish I can achieve success” to ” I look forward to becoming an invaluable addition to your establishment” ...out of time here…somone else will have to take over the closing….

My version:

Thank you for offering me the position of supervisor at your company.
You impressed me with your enthusiasm for the restaurant. I am confident you will build a successful team and provide a pleasant working environment for the staff. I hope to achieve success under your guidance.
Enclosed is my document, I think you will find it satisfactory.
Thank you again and I am looking forward to working with you.

Best regards,
Man

Thank you for offering me the position of supervisor at your company. I accept your offer, and I look forward to working with you.

You really impressed me with your enthusiasm in the restaurant. I am sure that you can build up a successful team and provide a good working environment in a profitable and popular establishment. I look forward to participating in that venture, and I hope to contribute to your success.

I have sent you my document, which is attached to this email.

Best regards,
Man

The minor corrections as noted, and you really have to say “yes, I accept” at some point.

Congratulations and good luck.

I don’t know if in your job there are times that you have to write memos or reports or stuff like that, but i advice you (sincerely, i am not being mean here) to have a dictionary by hand.
It could give a sloppy impression if there are little mistakes in your texts.
If you are not sure about a word, just check it and correct it if necessary.

I assume you are accepting. I would add a line

“I would like to take this opportunity to formally accept your offer.”

@Coloma I think he should keep the letter in the active voice; it’s more professional, and makes the author seem more in control.