You know that the light from the sun, falling on the moon can be considered parallel, so, if the moon's surface were a specular/regular reflector, it would give off a parallel, narrow, directed reflected beam.
So, this light would fall on a particular small region of earth only, and that too very occasionally! As this is not what we observe, it is obvious that the moon reflects the sunlight in all random directions, aka, a diffused reflector!