FOIL

First of all, you have to know how to add, subtract, and multiply integers. The easiest way to show how to do this is to work out a few examples.
x2+5x+6
This is pretty basic. We are looking for two numbers that add to 5 and multiply to 6. Of course, the numbers are 2 and 3. So our factored expression is (x+2)(x+3). The numbers you would put in the four solution boxes are 1,2,1,3 because the coefficient in front of the x is understood to be 1.