jmc

There are four possible ways the plywood can be cut: all the cuts are parallel to the length, all the cuts are parallel to the width, one cut is parallel to the length and one parallel to the width, or two cuts are parallel to the width and one is parallel to the length. In the first way, the congruent rectangles have dimensions $2\times 4$, for a perimeter of $2+2+4+4=12$ feet. In the second way, the congruent rectangles have dimensions $1\times 8$, for a perimeter of $1+1+8+8=18$ feet. In the third and fourth ways, the rectangles have dimensions $2\times 4$, for a perimeter of 12 feet. The positive difference between the greatest perimeter and the least is $18-12=\boxed{6}$ feet.