1. The original point is given as $(8, 2)$. This means $x=8$ and $y=2$ where $y=f(x)$. 2. The transformation is $y = -3f(-4x)$. We need to find the new coordinates after applying this transformation to the point $(8, 2)$. 3. First, find the new $x$ value inside the function: replace $x$ by $8$ in $-4x$, so the new input to $f$ is $-4 \times 8 = -32$. 4. The original function value at $x=8$ is $f(8) = 2$. We want to find the new $y$ value which is $-3f(-4 \times 8) = -3f(-32)$. 5. Since we do not know $f(-32)$ directly, but the problem implies the transformation applies to the point $(8, 2)$, we interpret that the point $(8, 2)$ corresponds to $f(8) = 2$, so the transformed point corresponds to $x=8$ mapping to $x' = -4 \times 8 = -32$ and $y' = -3 \times f(-32)$. 6. To find the new point, we consider the inverse of the $x$ transformation: the new $x$ coordinate is $x' = 8$, so the original $x$ is $x = -\frac{x'}{4} = -\frac{8}{4} = -2$. 7. Now, $f(-2)$ is the original function value at $x=-2$. Since we don't have $f(-2)$, but the problem only gives the point $(8, 2)$, we assume the transformation applies to the point $(8, 2)$ directly, so the new $x$ coordinate is $x' = 8$, and the new $y$ coordinate is $y' = -3 \times f(-4 \times 8) = -3 \times f(-32)$. 8. Without additional information about $f$, the problem likely wants the transformed point of $(8, 2)$ under $y = -3f(-4x)$, which is $(x', y') = \left(8, -3 \times 2\right) = (8, -6)$. 9. However, the $x$ coordinate also changes due to the $-4x$ inside $f$. The new $x$ coordinate is the original $x$ value that maps to $8$ after the transformation, so $x' = -4x = 8 \Rightarrow x = -2$. 10. So the new point is $(x', y') = (8, -3f(-4 \times (-2))) = (8, -3f(8)) = (8, -3 \times 2) = (8, -6)$. 11. Therefore, the new point after the transformation is $(8,-6)$.