The length of a rectangle is twice its width. if the perimeter of the rectangle is 42 inches , find its length and width.

The perimeter of a rectangle (or any figure, for that matter) is the sum of the lengths of its sides.
   P = L + W + L + W
   P = 2(L + W)

Your problem statement tells you L = 2W, so you can make the substitution of given information to get
   P = 2(2W +W)
   P = 6W
   42 in = 6W
   (42 in)/6 = W = 7 in

The length is twice that, so is 2*(7 in) = 14 in.

The length is 14 in.
The width is 7 in.