Explanation: To solve this problem, we need to determine the positions of the Ancient history book and the Medieval history book in the row of 64 books and then calculate the number of books between them.
1. **Position of Ancient History Book:**
- The Ancient history book is 25th from the left.
- This means there are 24 books to the left of it.
2. **Position of Medieval History Book:**
- The Medieval history book is 30th from the right.
- This means there are 30 books to the right of it.
- To find its position from the left, we subtract 30 from the total number of books (64) and add 1 (since the position is inclusive):
\[
\text{Position from left} = 64 - 30 + 1 = 35
\]
- So, the Medieval history book is 35th from the left.
3. **Number of Books Between:**
- To find the number of books between the 25th and 35th books, we subtract the position of the Ancient history book from the position of the Medieval history book and then subtract 1 (since we do not count the books themselves):
\[
\text{Number of books between} = 35 - 25 - 1 = 9
\]
Thus, the number of books between the Ancient history book and the Medieval history book is 9. This is why option D is the correct answer.
Understanding the positions from both ends and correctly calculating the difference is crucial in solving such problems. It is important to remember to subtract 1 from the difference to exclude the books themselves from the count.