How does estimation you place the decimal point in a product correctly? explain your reasoning

Here is an explanation using an example.
You are asked to multiply 4.88 by 3.12 by long multiplication.
You get the number 152256 before you place the decimal point.

Now by estimation, you see that 4.88 is close to 5, and 3.12 is close to 3.
Since 5 * 3 = 15, you know that 4.88 times 3.12 must be close to 15.

You look again at your long division result, 152256, and you know the decimal point must be placed between the 5 and the 2 because that makes the product 15.2256 which is close to 15.

If you place the decimal point in any other position, and you answer 1.52256, 152.256, 1522.56, 15225.6, or 152256, the answer is incorrect because none of those answers are as close to 15 as 15.2256 is. The estimated answer of 15 helped you place the decimal point in the correct place.

I’m not absolutely sure but i think it’s 7x6x5x4x3x2=5040 because as the first character you can take any of the 7 given then you are left with 5 then 6 then 4 etc.