Let \(\overline{abc}\) be the number\(\left(a,b,c\in\left\{4;6;0;8\right\};a\ne0\right)\) so that a,b,c are distinct.We have :

There are : 4 - 1 = 3 choices to choose a (since \(a\ne0\))

There are : 4 - 1 = 3 choices to choose b (since \(b\ne a\))

There are : 4 - 2 = 2 choices to choose c (since a,b,c are distinct)

So,the number of satisfied numbers we can form is : 3 x 3 x 2 = 18

Using the hundreds digit 4, we have 6 numbers: \(406;408;460;468;480;486\)

Using the hundreds digit 6, we have 6 numbers: \(604;608;640;648;680;684\)

Using the hundreds digit 8, we have 6 numbers: \(804;806;840;846;860;864\)

If the hundreds digit is 0, then the numbers are not the 3-digit-number.

So there are: \(6+6+6=18\left(numbers\right)\)

There are three ways to choose hundred of digits 

There are three dozen digit selectors

There are two ways to select the unit - number 

It is possible to write three digit whole number 

3 x 3 x 2 = 18 ( number )