Let's simplify the expression step-by-step:
The given expression is:
[tex]\[ 3\left(2x^2 + 4\right) - 4(x - 6) \][/tex]
1. First, simplify inside the brackets:
- [tex]\( 3(2x^2 + 4) \)[/tex] remains as it is.
- For [tex]\( -4(x - 6) \)[/tex], distribute the [tex]\(-4\)[/tex] through the terms inside the brackets:
[tex]\[ -4(x - 6) = -4 \cdot x + -4 \cdot (-6) \][/tex]
[tex]\[ = -4x + 24 \][/tex]
2. Next, we expand the terms:
[tex]\[ 3(2x^2 + 4) = 3 \cdot 2x^2 + 3 \cdot 4 = 6x^2 + 12 \][/tex]
So, the expression now is:
[tex]\[ 6x^2 + 12 - 4x + 24 \][/tex]
3. Finally, combine the like terms:
- [tex]\(6x^2\)[/tex] is the only [tex]\(x^2\)[/tex] term.
- Combine the constant terms: [tex]\(12 + 24 = 36\)[/tex]
- Keep the [tex]\(-4x\)[/tex] term as is.
Putting it all together:
[tex]\[ 6x^2 - 4x + 36 \][/tex]
Thus, the simplified expression is:
[tex]\[ 6x^2 - 4x + 36 \][/tex]
So, the correct answer is:
[tex]\[ \boxed{6x^2 - 4x + 36} \][/tex]
