Answer
See the picture below.
Work Step by Step
The parent function is $f(x)=(\frac{1}{3})^x$ (with red) the given function is $g(x)=(\frac{1}{3})^{x-4}$ (with blue).
The parent function can be graphed by calculating a few coordinates and connecting them with a smooth curve:
$f(-2)=(\frac{1}{3})^{-2}=9$
$f(-1)=(\frac{1}{3})^{-1}=3$
$f(0)=(\frac{1}{3})^0=1$
$f(1)=(\frac{1}{3})^1=\frac{1}{3}$
$f(2)=(\frac{1}{3})^2=\frac{1}{9}$
For every corresponding x-value the following equation is true: $f(x-4)=g(x)$
This means that the graph is translated 4 units right
($g(x)$ involves a horizontal shift of 4 to the right).
Because when f(x)=g(x), the g(x) function acts like the f(x).
For example if $f(0)=1$ in the original $f(x)$, this will be equal to $g(4)=f(4-4)=f(0)=1$. $Here, f(0)=g(4)$ also, $f(1)=g(5)$
We can see that here, each point in the parent function was moved to the right by 4 units.