Let l be the length and w be the width of the rectangle.
It is given that the perimeter is 72 cm.
Therefore, 2(l + w) = 72
Divide both sides by 2.
l + w = 36
It is also given that the length l is 6 cm longer than the width, w.
Therefore, l = w + 6
Now, (w + 6) + w = 36
(w + w) + 6 = 36
2w + 6 = 36
2w = 36 - 6
2w = 30
Divide both sides by 2.
w = 15
Hence, the width of the rectangle is 15 cm. and it is given in option C.