1. **State the problem:** We have triangle $\triangle ABC$ with vertices $A(-4,4)$, $B(-3,2)$, and $C(-2,3)$. We want to find the coordinates of $\triangle A''B''C''$ after reflecting $\triangle ABC$ over the $y$-axis and then dilating it by a scale factor of 3 about the origin. 2. **Reflection over the $y$-axis:** Reflecting a point $(x,y)$ over the $y$-axis changes its $x$-coordinate to $-x$ while keeping $y$ the same. So, $$A' = (4,4), \quad B' = (3,2), \quad C' = (2,3)$$ 3. **Dilation by scale factor 3 about the origin:** Dilating a point $(x,y)$ by scale factor $k=3$ about the origin multiplies both coordinates by 3: $$A'' = (3 \times 4, 3 \times 4) = (12,12)$$ $$B'' = (3 \times 3, 3 \times 2) = (9,6)$$ $$C'' = (3 \times 2, 3 \times 3) = (6,9)$$ 4. **Check the options:** The vertices after transformations are $(12,12)$, $(9,6)$, and $(6,9)$. None of the given options exactly match these points. 5. **Re-examine the problem:** The options given are multiples of the original reflected points but scaled by 3. The closest matching option is $(9,9)$, $(3,6)$, and $(0,12)$ which does not match our calculation. 6. **Conclusion:** The correct transformed vertices are $A''(12,12)$, $B''(9,6)$, and $C''(6,9)$, which are not listed among the options. Possibly a misprint or error in the options. **Final answer:** The vertices of $\triangle A''B''C''$ are $$A''(12,12), B''(9,6), C''(6,9)$$