The latent heat of vaporization of water is more than latent heat of fusion of ice, because :
on vaporization much larger increase in volume takes place
increase in kinetic energy is much larger on boiling
kinetic energy decreases on boiling
volume decreases when the ice melts
The correct option is B increase in kinetic energy is much larger on boiling
In solids, the molecules are very close together and the attraction between the molecules are great. This causes a substance to have a structure in which the molecules have little freedom to move, as you would see in the case of ice. In the case of a liquid, the molecules are closely spaced, though not as closely spaced as a solid, they have more freedom to move and the intermolecular forces are weaker that that of a solid. Thus a liquid can flow, unlike a solid. Now in a gas, the molecules are sufficiently far apart that there are little to no attractive forces. Because of this a gas can easily be compressed and take the shape of the container.
Now as you heat a solid turning it into a liquid, you increase the kinetic energy of its molecules, moving them further apart until the forces of attraction are reduced to allow it to flow freely. Keep in mind the forces of attraction still exists. Now as you heat a liquid, turning it into a gas, the kinetic energy of the molecules are increased to a point where there are no forces of attraction between the molecules.
The energy required to completely separate the molecules, moving from liquid to gas, is much greater than if you were just to reduce their separation, solid to liquid. Hence the reason why the latent heat of vapourization is greater that the latent heat of fusion.