There are 172 different arrangements.
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There are 12 two letter arrangements of the letters in PARK.
Only 20.
Assuming you don't repeat letters:* 7 options for the first letter * 6 options for the second letter * 5 options for the third letter * 4 options for the fourth letter (Multiply all of the above together.)
If all the letters are unique in the set, there are 6 choices for the first letter, 5 for the second letter, 4 for the third letter, etc. This results in 6 X 5 X 4 X 3 X 2 = 720 arrangements. If some of the six letters are duplicated, there will be fewer distinct arrangements.
Infinitely many. You could, for example, cut out images of the 8 letters and paste then on the wall facing you. Each letter can take infinitely many positions on that wall so you have infinitely many arrangements.