There are 4 ways to choose the first letter.

For each of the 4 ways to choose to choose the 1st letter, there are
3 ways left to choose for the second letter. That's 4×3 or 12 ways to
choose the first two letters.

For each of the 4×3 or 12 ways to choose to choose the first two letters,
there are 2 ways left to choose for the third letter. That's 4×3×2 or 24 ways 
to choose the first three letters.

For each of those 4×3×2 ways to choose the first three letters, there is
just 1 way to choose the fourth letter. That's 4×3×2×1 or still 24 ways
to choose all 4 letters.  Here are all 24 ways:

 1. MATH
 2. MAHT
 3. MTAH
 4. MTHA
 5. MHAT
 6. MHTA
 7. AMTH
 8. AMHT
 9. ATMH
10. ATHM
11. AHMT
12. AHTM
13. TMAH
14. TMHA
15. TAMH
16. TAHM
17. THMA
18. THAM
19. HMAT
20. HMTA
21. HAMT
22. HATM
23. HTMA
24. HTAM

Edwin