Sure, let's simplify the expression step-by-step:
Given expression:
[tex]\[ -3(6-2) + |-4| \div 2 \][/tex]
Step 1: Simplify the expression inside the parentheses.
[tex]\[
6 - 2 = 4
\][/tex]
The expression now is:
[tex]\[
-3(4) + |-4| \div 2
\][/tex]
Step 2: Apply the multiplication.
[tex]\[
-3 \times 4 = -12
\][/tex]
So the expression becomes:
[tex]\[
-12 + |-4| \div 2
\][/tex]
Step 3: Evaluate the absolute value and the division.
The absolute value of [tex]\(-4\)[/tex] is [tex]\(4\)[/tex]:
[tex]\[
|-4| = 4
\][/tex]
Now perform the division:
[tex]\[
4 \div 2 = 2
\][/tex]
The expression updates to:
[tex]\[
-12 + 2
\][/tex]
Step 4: Simplify the final expression.
[tex]\[
-12 + 2 = -10
\][/tex]
Therefore, the simplified result is:
[tex]\[
\boxed{-10}
\][/tex]
