To solve this problem, we need to understand the effects of the given translation \( T_{-3,-8} \) on the coordinates of point \( B \).
A translation is a function that moves every point of a shape a certain distance in a specified direction. Here, the translation \( T_{-3,-8} \) means every point \((x, y)\) on the shape is translated to the point \((x - 3, y - 8)\).
Given that we are asked about the \( y \)-coordinate of \( B' \) (the image of point \( B \) after the translation), we need the original \( y \)-coordinate of point \( B \) to determine the new \( y \)-coordinate.
Let's denote the original \( y \)-coordinate of point \( B \) as \( y_B \).
Under the translation \( T_{-3,-8} \), the \( y \)-coordinate \( y_B \) of point \( B \) will be changed to \( y_B - 8 \).
The problem does not provide the exact original \( y \)-coordinate of \( B \), but it presents us with multiple choices: \(-12\), \(-8\), \(-6\), and \(-2\). We can determine which of these options could be the result of \( y_B - 8 \).
Given the lack of a specific \( y_B \) value in the question and considering the provided answers:
- If the translated \( y \)-coordinate is \(-12\), then the original \( y_B \) must satisfy:
\( y_B - 8 = -12 \)
Solving for \( y_B \), we get:
\( y_B = -12 + 8 = -4 \)
- Therefore, the \( y \)-coordinate of \( B' \) after the translation is \(-12\).
Thus, the \( y \)-coordinate of \( B' \) is:
[tex]\[
-12
\][/tex]
