Answer
$360$ different arrangements.
Work Step by Step
1) It is not a sequence of choices
2) The order in which the letters are chosen matters
3) Only 4 of the 6 letters are used
4) The letters are distinct
Permutation of 6 distinct letters taken 4 at a time:
$_6P_4=\frac{6!}{(6-4)!}=\frac{6!}{2!}=\frac{6\times5\times4\times3\times2\times1}{2\times1}=6\times5\times4\times3=360$