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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.
There are 12 two letter arrangements of the letters in PARK.
There are 172 different arrangements.
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.)
The number is 26*25*24 = 15600.