Lucky's generalization that an 8's fact can be broken down into 4x2 is not necessarily correct. While it is true that the multiplication of 4 and 2 will indeed yield 8, it doesn't always mean that the result is a multiple of 8.
Multiplication, in mathematics, is associative. This means that the grouping of numbers in an expression does not affect the result. For instance, if you have the numbers 2, 3, and 4, you can group them in any way you want, and the result will always be the same. You can multiply 2 and 3 first and then multiply the result by 4, or you can do it the other way around, multiply 3 and 4 first and then multiply the result by 2. The end result will still be the same.
The reason why Lucky's generalization isn't correct lies in the fact that while 4x2 is equal to 8, it doesn't mean that any multiplication of 4 and 2 will always yield a multiple of 8.
So the statement "an 8's fact can be broken into 4x2" is false.