The question is related to the relationship between stopping distances of a truck, a car, and a motorcycle when they have equal kinetic energies. The kinetic energy is given by the formula 1/2 mv^2, where m is mass and v is velocity. The stopping distance for a vehicle is directly proportional to the square of its velocity.

Option 1, x > y > z, suggests the truck requires the longest stopping distance and the motorcycle the shortest. This would be incorrect as it does not consider the equal kinetic energies. Same is with option 2, x < y < z, which suggests the truck requires the shortest stopping distance and the motorcycle the longest distance.

Option 4, x 4y 8z, does not make sense as it appears to suggest some sort of numerical relation which contradicts the principle of equal kinetic energies.

The correct answer is option 3, x = y = z. This means the stopping distances for all three vehicles are equal, which aligns with the condition presented in the question of equal kinetic energies. Despite differences in size and mass, because their kinetic energies are equal, their stopping distances will also be equal. So, the correct option is x = y = z.