The problem says we have a square flower bed to start out with.
Let's have the sides of the squares be "x". The area of this original flower bed is
.
Then, one side of the square is enlarged by 2ft, and another side 3ft. Our new flower bed dimensions are now (x+2) and (x+3). Multiply (x+2) and (x+3) to find the area, which gets you
.
We also know that the new area of the flower bed is twice the size of the original flower bed. Multiply the original area by 2, you get
.
With the new area and the doubled original area, we can now make an equation: 
Solve for x, you get 6.
Hope this explanation helped, maybe a bit too many details but there's your answer, 6!