We need to go some Pythagoras' Theorem, but for 3D.

Fortunately the simplified formula for 3D is straightforward.

Length of diagonal in 2D is sqrt (x² + y²)
Length of diagonal in 3D is sqrt (x² + y² + z²)

Here, the longest stick would span the furthest distance in the box which is from one corner of the box to the exact opposite corner of the box.

For Box A, this length is sqrt (8² + 5² + 4²), which is sqrt 105.

For Box B, this length is sqrt (7² + 7² + 1²), which is sqrt 99.

Clearly sqrt 105 > sqrt 99, so the claim is not true.