1. This is the my book.

2. This is the book of mine.

3. Look at the these book.
4. Bring some the books.
5. Bring the some books.
6. Take the every book.
7. Take the any books.
8. Take each the book.
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Is only #2 grammatical? What about the others?

To determine if the given sentences are grammatically correct, we need to examine each one individually:

1. This is the my book.
This sentence is grammatically incorrect. The word "the" is unnecessary, and there should be no possessive pronoun before "my." Instead, it should be "This is my book."

2. This is the book of mine.
This sentence is grammatically correct. "Book of mine" is a possessive construction and is used to indicate ownership. Although it is less common to use "of mine" to indicate possession, it is still grammatically valid.

3. Look at the these book.
This sentence is grammatically incorrect. The word "the" is not necessary, as "these" already implies that it is referring to specific books. Additionally, "book" should be pluralized to "books." The correct form would be "Look at these books."

4. Bring some the books.
This sentence is grammatically incorrect. The word "some" is redundant and should be removed. The correct form would be "Bring the books," assuming there is a specific set of books that the speaker wants to be brought.

5. Bring the some books.
This sentence is grammatically incorrect. The word "the" before "some" is unnecessary and should be removed. The correct form would be "Bring some books," which implies a non-specific quantity of books.

6. Take the every book.
This sentence is grammatically incorrect. The word "the" is unnecessary before "every." Instead, it should be "Take every book" to express the idea of taking all the books in general.

7. Take the any books.
This sentence is grammatically incorrect. The word "the" before "any" is unnecessary, as "any" is already a determiner. The correct form would be "Take any books," which suggests taking an unspecified number of books.

8. Take each the book.
This sentence is grammatically incorrect. The word "the" should be removed before "each." The correct form is "Take each book," which implies taking one book at a time.

In summary, sentence #2 is grammatically correct, while the others have one or more errors that need to be corrected for proper grammar.