If the area of the smaller rectangle is $2x$, the area of the larger rectangle is $4x$, and the height of the larger rectangle is $4x/6$. The height:length ratio of both rectangles must be the same, since they are similar.
So $\frac{2}{x} = \frac{4x}{36}$
$x^{2} = 18$
$x=\sqrt{18}$
Alternatively, call the height of the larger rectangle $y$.
Then, comparing the areas, $4x = 6y$
By similarity, $\frac{y}{2} = \frac{6}{x}$
i.e. $y = \frac{12}{x}$
Then by substitution, $4x = \frac{72}{x}$
$x^{2} = 18$
$x = \sqrt{18}$