A garden has the shape of a rectangle. This garden is enlarged to create a new garden. Its width is doubled and its length is tripled. How many times larger is the area of the new garden than the area of the old garden?

Step 1 ：Let the width of the old garden be W and the length be L.

Step 2 ：The width of the new garden is doubled, so it is 2W.

Step 3 ：The length of the new garden is tripled, so it is 3L.

Step 4 ：The area of the old garden is \(A_{old} = W \times L\).

Step 5 ：The area of the new garden is \(A_{new} = (2W) \times (3L) = 6WL\).

Step 6 ：The ratio of the area of the new garden to the area of the old garden is \(\frac{A_{new}}{A_{old}} = \frac{6WL}{WL} = 6\).

Step 7 ：\(\boxed{6}\) times larger is the area of the new garden than the area of the old garden.