Solving this requires external resources.
The fact that both the problem and the answer are expressed as numbers is largely a red herring.
Thanks to reading a lot of books and hint #2, the answer is:
The clue is made up of
4 ISBN-10 numbers
0870678884 - How to Win
0689834098 - You Have to Write
1582403988 - Six
0670002291 - Times Three