Certainly! Let's solve the problem step-by-step.
We are given the expression:
[tex]\[ 4(x^2 + 3) - 2y \][/tex]
We need to evaluate this expression for [tex]\( x = -6 \)[/tex] and [tex]\( y = -\frac{1}{2} \)[/tex].
### Step 1: Substitute [tex]\( x = -6 \)[/tex] and [tex]\( y = -\frac{1}{2} \)[/tex] into the expression
First, we substitute [tex]\( x = -6 \)[/tex]:
[tex]\[ x^2 = (-6)^2 = 36 \][/tex]
Now substitute this back into the expression:
[tex]\[ 4(x^2 + 3) - 2y = 4(36 + 3) - 2(-\frac{1}{2}) \][/tex]
### Step 2: Simplify inside the parentheses
Calculate inside the parentheses:
[tex]\[ 36 + 3 = 39 \][/tex]
So, the expression now reads:
[tex]\[ 4 \cdot 39 - 2(-\frac{1}{2}) \][/tex]
### Step 3: Multiply and simplify
Next, we perform the multiplication:
[tex]\[ 4 \cdot 39 = 156 \][/tex]
And simplify the -2 times [tex]\(-\frac{1}{2}\)[/tex]:
[tex]\[ -2 \times -\frac{1}{2} = 1 \][/tex]
So the expression now reads:
[tex]\[ 156 + 1 = 157 \][/tex]
Therefore, the value of the expression is:
[tex]\[ \boxed{157} \][/tex]
So, the correct answer is:
D. 157
