Suppose U = {1, 2, 3, 4, 5, 6, 7, 8} is the universal set and P = {1, 2, 3, 4}. What is P?

Did you mean P'? The letter P with a tick mark after it. If so, then start with set U and erase any number you find in set P

We start with

{1,2,3,4,5,6,7,8}

and we erase the following: 1,2,3,4

since those numbers are in set P

P = {1,2,3,4}

P ' = {5, 6, 7, 8}

The set P' is the complement of set P. It is, in a sense, the opposite of set P. It contains everything that P doesn't have.