To determine the percent increase in the area of the rectangle garden plot, we need to calculate the original area and the new area after increasing the length and width by 20%.

Let's assume the original length is L and the original width is W. The original area is given by A = L * W.

After increasing the length and width by 20%, the new length becomes 1.2L (20% increase) and the new width becomes 1.2W (20% increase). The new area is given by A' = 1.2L * 1.2W = 1.44LW.

The percent increase in the area is calculated as ((A' - A) / A) * 100.

Substituting the values, we get ((1.44LW - LW) / LW) * 100 = (0.44LW / LW) * 100 = 44%.

Therefore, the percent increase in the area of the plot is 44%.

The correct answer is (E) 44%.