1. Check the tree diagram in the attached picture.
2. The first Letter can be one of the letters I, O , W or A. Assume your first letter is I, then you have 3 choices for the second letter, that is O, W or A.
3. Assume you pick O, then you have 2 options for the third letter; W or A.
4. If you pick A, then the last letter can only be W.
5. the path described is the "red line path" in the picture; that is the arrangement IOAW.
6. Another path is the "dashed line path" IAOW.
7. We count 6 "paths", where I is the first letter, each "path" standing for one arrangement.
8. 4*6=24 is the total number of paths, that is arrangements of the letters IOWA.
9. Remark: The first choice is 4, combined (multiplied) by 3 choices for the second letter, combined (multiplied) by 2 choices for the third and finally multiplied by 1.
10. Thus there are 4*3*2*1 arrangements of 4 (different) letters.