To find the [tex]\(y\)[/tex]-intercept of the graph of the equation [tex]\( y = 6 \left(x - \frac{1}{2}\right)(x + 3) \)[/tex], we need to determine the value of [tex]\(y\)[/tex] when [tex]\(x = 0\)[/tex].
To do this:
1. Substitute [tex]\(x = 0\)[/tex] into the equation:
[tex]\[
y = 6 \left(0 - \frac{1}{2}\right)(0 + 3)
\][/tex]
2. Simplify inside the parentheses:
[tex]\[
y = 6 \left(-\frac{1}{2}\right)(3)
\][/tex]
3. Perform the multiplication:
[tex]\[
y = 6 \times -\frac{1}{2} \times 3
\][/tex]
4. Simplify the multiplication step-by-step:
[tex]\[
y = 6 \times -\frac{1}{2} = -3
\][/tex]
[tex]\[
y = -3 \times 3 = -9
\][/tex]
So, the [tex]\(y\)[/tex]-intercept is [tex]\(-9\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{-9}
\][/tex]
