1. The problem asks for the function $g(x)$ which is the reflection of $f(x) = 6 \left(\frac{1}{3}\right)^x$ across the y-axis. 2. Reflection across the y-axis means replacing $x$ by $-x$ in the function. So, if $f(x) = 6 \left(\frac{1}{3}\right)^x$, then $$g(x) = f(-x) = 6 \left(\frac{1}{3}\right)^{-x}$$ 3. Using the property of exponents $a^{-x} = \frac{1}{a^x}$, we rewrite: $$g(x) = 6 \left(\frac{1}{3}\right)^{-x} = 6 \cdot 3^x$$ 4. Therefore, the reflected function is $$g(x) = 6 \cdot 3^x$$ 5. Among the options given, this corresponds to $g(x) = 6(3)^x$. 6. This matches the graph description where $g(x)$ grows as $x$ increases negatively (since $3^x$ grows rapidly for positive $x$ and decays for negative $x$, reflecting $f(x)$ across the y-axis swaps this behavior).