You have six choices for the first digit (any of 4, 5, 6, …, 9). For any of these initial digits, you have five choices for the second digit (Any EXCEPT the one used already in the thousands place). There are, consequently, four choices for the third digit and three choices for the fourth digit (any digit not already used). So, in all,
6
⋅
5
⋅
4
⋅
3
=
360 such four-digit numbers.
