Choose the first digit any of the 4 ways.
Then choose the second digit any of the remaining 3 unchosen digits.
Then choose the third digit either of the remaining 2 unchosen digits.
Then choose the fourth digit as the only 1 remaining unchosen digit.

Answer  ways.

Here are all 24 4-digit numbers that can be made with them:

 1.  3678
 2.  3687
 3.  3768
 4.  3786
 5.  3867
 6.  3876
 7.  6378
 8.  6387
 9.  6738
10.  6783
11.  6837
12.  6873
13.  7368
14.  7386
15.  7638
16.  7683
17.  7836
18.  7863
19.  8367
20.  8376
21.  8637
22.  8673
23.  8736
24.  8763

Edwin