To find the dimensions of a cuboid from its volume, we factorize the given volume expression into three factors, representing length, breadth, and height. For part (i), we factorize $6a^{2}$ - $24b^{2}$ by taking out the common factor 6, and then applying the difference of squares identity. For part (ii), we take out the common factor 3p from $3ps^{2}$ - 15ps + 12p, and then factorize the resulting quadratic trinomial by splitting the middle term.