There are 4 ways to choose the first digit.

For each of those 4 ways, that leave 3 ways to choose the 
second digit.

So that's 4×3 or 12 ways to choose the first two digits.

For each of those 4×3 ways to choose the first two digits,
that leave 2 ways to choose the third digit.

So that's 4×3×2 or 24 ways to choose the first three digits.

For each of those 4×3×2 ways to choose the first three digits,
that leaves just 1 way to choose the last digit.

So that's 4×3×2×1 or 24 ways to choose all four digits.

Here they all are:

1.  1468
2.  1486
3.  1648
4.  1684
5.  1846
6.  1864
7.  4168
8.  4186
9.  4618
10.  4681
11.  4816
12.  4861
13.  6148
14.  6184
15.  6418
16.  6481
17.  6814
18.  6841
19.  8146
20.  8164
21.  8416
22.  8461
23.  8614
24.  8641

Edwin