Question 123789
This one was hard for me to picture in my head, too, so I drew a picture on paper.  I suggest you do the same, or the following will make little to no sense.  I drew a rectangle and then labeled one side 20 and the other 12.  Then I drew a square in each corner, and labeled each edge not on the rectangle's edge x.  So each square has 2 x's.  Now those are the squares that will be cut off, and the small rectangles sticking out to the side will be folded up to make the sides of the box.  So I drew in the base of that box by continuing the lines that are there from the squares.  Now I looked at that centered rectangle.  The area of that should be 84.  The length is 20-2x and the width is 12-2x.  So (20-2x)(12-2x)=84.
240-64x+4x^2=84
Divide by 4: 40-16x+x^2=21
x^2-16x+39=0
Factor: (x-3)(x-13)=0
x can't be 13 because the width of the big rectangle is only 12, and we are cutting off x from each end.  So x=3.  So you need to cut off a 3x3 square at each corner.