Given:
Sarah is planning two gardens.
The smaller garden has a width of 9 ft and a length of 12 ft.
The length of the larger garden is 4 ft longer than the length of the smaller garden.
So, the length of the larger garden = 12 + 4 = 16
Let the width of the larger garden = x
The length and width of the larger garden are in the same proportion to the length and width of the smaller garden.
so,

solve for x:

so, the width of the larger garden = 12 ft