Given that the sides of a box are 6 X 8 X 24 cm.

Then, we know that the longest part of the box is the diagonal.

Then we need to calculate the diagonal.

The diagonal is:

D = sqrt( a^2 + b^2 + c^2 ) where a , b, and, c are the sides of the box:

==> D = sqrt( 6^2 + 8^2 + 24^2)

==> D = sqrt( 36 + 64 + 576)

==? D = sqrt( 676)

==> D = 26

**Then, the longest stick that we can fit in the box is 26 cm .**

We are given a rectangular box with the dimensions 6 cm, 8 cm and 24 cm. We have to find the length of the longest stick that can be placed in the box.

This length is equal to the diagonal of the box. We can calculate the length of the diagonal of a rectangular box of sides A, B and C by the expression sqrt (A^2 + B^2 + C^2). Here this is equal to sqrt (6^2 + 8^2 + 24^2).

sqrt (6^2 + 8^2 + 24^2) = sqrt (36 + 64 + 576) = sqrt (676) = 26 cm.

**The required length of the longest stick is 26 cm.**