ROC of Z Transform of $x(n) = 2(3)^nu(-n)$
Using the definition, and letting $k=-n$:

$X(z)=2 \sum_{n=-\infty}^03^nz^{-n}=2\sum_{k=0}^{\infty}\big(\frac{1}{3}z\big)^k$

Now we can use the geometric series (https://en.wikipedia.org/wiki/Geometric_series) formula only if we require $|\frac{1}{3}z|&lt;1$, or equivalently $|z|&lt;3$