This is not quite correct, because we have overcounted. The answer
of 3024 would be correct if the atoms had names or labels, and if
arrangements of the type shown at the lower left really were different.
But atoms have no labels.
If by some miraculous process we could photograph the atoms at
a chosen instant and study them, we could tell the difference between
the four arrangements at the upper left because the atoms would
occupy different places.
However, we could see absolutely no difference in the twelve arrangements
at the middle left, because one atom is just like every other atom
of the same type. The most that we could say is that atoms were
present at Positions 3, 4, 7, and 8 of our mini-universe.