Please be careful when typing in the problem. You state that the perimeter is only 46 cm, yet the length is 4 m longer than the width. That added 4 m on a single side is 8.7 times LONGER than the entire perimeter, without using the yet to be determined width and length.
The equation P = 2L + 2W can be simplified by dividing by 2: P/2 = L + W
(3w+ 4) + w = 23 < half the perimeter
4w = 19
w = 19 / 4 = 4.75
l = (3 * 4.75) + 4 = 18.25