Final answer:
The space between the boards laid across the joists and the roof of the small shed was a very small garret, occupied by rats. So, the correct answer is option d.
Step-by-step explanation:
In the provided passage, the space located between the boards laid across the joists at the top of the small shed attached to the grandmother's house and the roof was a very small garret. This garret was never occupied by anything but rats. Therefore, the correct answer to what was located between the boards and the roof is roof.
So, the correct answer is option d.