If 5472 implies 9, 6342 implies 6, 7584 implies 6 and 9237 implies P, then P is: (implies means the digits are summed and reduced to a single digit)

P equals 3.

Each number's digits are added and then reduced to a single digit.

5+4+7+2 = 18, then 1+8 = 9; 6+3+4+2 = 15, then 1+5 = 6.

7+5+8+4 = 24, then 2+4 = 6, matching the given results.

9+2+3+7 = 21, then 2+1 = 3, so P = 3.