Analysis:

Method 1. (solving equations)

Let t=x*3, then: (X*3)*2=3660 can be changed to: t*2=3660, where t > 0.

According to the regulation: a * b = a (a+1) (a+2) ... (a+b-1), we can get:

t(t+ 1)=3660

t？ +t-3660=0

Factorization:

(t-60)(t+6 1)=0

The solution is t=60 (t=-6 1 irrelevant, so it is discarded).

So: x * 3 = 60.

Then: x(x+ 1)(x+2)=60.

It is easy to solve x=3.

Method two. Because (X*3)*2=3660, we know that:

Two adjacent natural numbers x*3 and x*3+1 are multiplied to get 3660.

Then the product of such natural numbers is 60*6 1=3660.

So: x*3=60.

X*3 is the product of three consecutive natural numbers x, X+ 1 and X+2, which is 60.

Since: 3*4*5=60, therefore:

Easy to get: x=3