Suppose the first one is X, and the last one is (X+ 1) (X+2)(X+3), and there are:

X (X+ 1) (X+2)(X+3) = 3024

Numbers must all be natural numbers, and the above four numbers are multiplied by the fourth power of X. If 3024 is raised to the fourth power, it is equal to about 7, then X should also be around 7. After testing, X=6 meets the meaning of the question.