What two numbers multiply to -48 and add to -8? You can list out all the possible combos through trial and error. The two values are -12 and 4 since...
-12 plus 4 = -8
-12 times 4 = -48
So because the values are -12 and 4, we know that x^2-8x-48 factors to (x-12)(x+4)
The factors are x-12 and x+4
The order in which you list the factors doesn't matter. You can multiply in any order.