To find the longest baton that could fit diagonally in the box, we need to find the length of the longest diagonal of the rectangular box.
Using the Pythagorean theorem, we can find the diagonal length:
diagonal length = sqrt(6^2 + 8^2 + 6^2)
= sqrt(36 + 64 + 36)
= sqrt(136)
≈ 11.66 inches
Therefore, the longest baton that could fit diagonally in the box is approximately 11.66 inches long.