The image shows a cube $PQRS.TUVW$ where $PQ = 6 \, \text{cm}$, and the question seems to be asking for a certain distance or length related to this cube, based on the options provided. Let me guide you through solving this.

Assumptions:

From the image, we see that $PQ = 6 \, \text{cm}$, meaning the side length of the cube is 6 cm. If the question is asking for the diagonal of the cube, we can use the formula for the space diagonal of a cube.

Formula for the space diagonal of a cube:

The space diagonal $d$ of a cube with side length $a$ is given by: $d = a\sqrt{3}$ where $a = 6 \, \text{cm}$.

Calculation:

$d = 6\sqrt{3} \, \text{cm}$

This length matches the structure of the provided answer choices. Thus, the correct answer is likely the one with the form $6\sqrt{3}$.

Would you like more details on the solution or help with another aspect of the problem?

Here are 5 related questions to deepen your understanding:

1. How do you calculate the length of the diagonal on a square face of a cube?
2. What is the relationship between the space diagonal and the face diagonal of a cube?
3. Can you calculate the surface area of a cube if you know the side length?
4. How do you find the volume of a cube from the side length?
5. How can you generalize the space diagonal formula for a rectangular prism?

Tip: For problems involving 3D shapes, try to identify which diagonal or segment is being asked about: face diagonal, space diagonal, or edge length.