1. The problem states that if $F(\omega)$ is the Fourier transform of $f(t)$, we need to find the Fourier transform $G(\omega)$ of the function $g(t) = -3 e^{6jt} f(t)$. 2. Recall the modulation property of the Fourier transform: if $g(t) = e^{jbt} f(t)$, then $G(\omega) = F(\omega - b)$. This means multiplying $f(t)$ by a complex exponential shifts the Fourier transform by $b$ in frequency domain. 3. In our problem, $g(t) = -3 e^{6jt} f(t)$, which is $f(t)$ multiplied by $-3$ and $e^{6jt}$. The constant $-3$ scales the Fourier transform by $-3$, and $e^{6jt}$ shifts the transform by $6$. 4. Therefore, the Fourier transform $G(\omega)$ can be expressed as $$G(\omega) = A F(\omega - b)$$ where $A = -3$ and $b = 6$. 5. Final answer: $$A = -3$$ $$b = 6$$