If the numerical values of the total surface area and the volume of a cube are equal, then the length of its diagonal is

Let the side length of the cube be $a$.
Total Surface Area $=6a^2$
Volume $=a^3$
Given that their numerical values are equal:

$$6a^2=a^3⟹a=6(\text{since }a\ne 0)$$

The formula for the length of the diagonal of a cube is $a\sqrt{3}$.
Substituting $a=6$:

$$\text{Diagonal}=6\sqrt{3}$$