#### Answer

$x=0.36$

#### Work Step by Step

To solve the given equation graphically, you have to treat each side of the equation as a function.
Thus, using a graphing utility, graph the functions:
$y=4^{-x}$ (blue graph)
$y=\sqrt{x}$ (the red graph)
(refer to the image below for the graph.
The point/s where the graphs intersect are the points where $4^{-x}=\sqrt{x}$.
The x-coordinates of these point are the solutions to the given equation.
Note that the graphs intersect at the point $(0.364, 0.604)$.
The x-coordinates of these points are $0.36$.
Rounded-off to two decimal places, the solution to the given equation is:
$x=0.36$.