Let's simplify the given expression step-by-step:
[tex]\[
\frac{\left|4^2 - 34\right|}{4} \cdot 6^2 - 12^2 - 14
\][/tex]
### Step 1: Calculate inside the absolute value
First, we need to compute [tex]\(4^2 - 34\)[/tex]:
[tex]\[
4^2 = 16
\][/tex]
Thus,
[tex]\[
4^2 - 34 = 16 - 34 = -18
\][/tex]
### Step 2: Apply the absolute value
Now, we take the absolute value:
[tex]\[
\left|-18\right| = 18
\][/tex]
### Step 3: Divide by 4
Next, divide 18 by 4:
[tex]\[
\frac{18}{4} = 4.5
\][/tex]
### Step 4: Multiply by [tex]\(6^2\)[/tex]
Now, multiply the result by [tex]\(6^2\)[/tex]:
[tex]\[
6^2 = 36
\][/tex]
Thus,
[tex]\[
4.5 \times 36 = 162
\][/tex]
### Step 5: Subtract [tex]\(12^2\)[/tex]
Next, we compute [tex]\(12^2\)[/tex] and subtract it from the previous result:
[tex]\[
12^2 = 144
\][/tex]
Thus,
[tex]\[
162 - 144 = 18
\][/tex]
### Step 6: Subtract 14
Finally, subtract 14:
[tex]\[
18 - 14 = 4
\][/tex]
Thus, the simplified value of the expression is:
[tex]\[
4
\][/tex]
Therefore, the correct answer is:
A) 4
