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Functions $f$ and $g$ are graphed in the $x y$-plane, where $f(x)=3(2)^{x}$ and $g(x)=3(2)^{x}-6$. If $(0, a)$ is the $y$-intercept of function $f$ and $(0, b)$ is the $y$-intercept of function $g$, then what is the value of $a-b$ ?