A rectangular quilt's length is twice the length of a rectangular picture, and the quilt's width is three times the width of the same picture. The area of the picture is 2 square feet. What is the area of the quilt, in square feet?
Since the quilt is twice as long, the area is twice as large when only considering that dimension.  Since it is also 3 times as wide, the area then triples (including the doubling of size due to the length).  Thus, the area of the quilt is $2 \times 3 = 6$ times larger, making for an area of $\boxed{12}$ square feet.