let the length of the pieces be 'x', 'y' and 'z', x>0, y>0, z>0

a 16 inch board is to be cut into 3 pieces

x + y + z = 16

2 of the pieces must be 4 feet shorter than the third piece, let 'x' and 'y' are the pieces that are 4 ft shorter the the third piece z:

since 1 ft = 12 in

x = z - 4*12

x = z - 48

y = z - 4*12

this means x = y

lets solve the system

x + x + z = 16

x = z - 48

we find negative solutions for x

x = - 10.66

lets go back to our problem

z = x + 48 and x>0 thus z > 48 in

while x + y + z = 16 that is z < 16 in

we have contradiction z > 48 in and z < 16 in thus the problem has no solution.