To simplify the given expression [tex]\(\sqrt{12} \cdot 4 \sqrt{3}\)[/tex], let's proceed step-by-step:
Step 1: Simplify [tex]\(\sqrt{12}\)[/tex].
[tex]\[
\sqrt{12} = \sqrt{4 \cdot 3} = \sqrt{4} \cdot \sqrt{3} = 2 \sqrt{3}
\][/tex]
Step 2: Substitute [tex]\(\sqrt{12}\)[/tex] with its simplified form in the expression.
[tex]\[
(2 \sqrt{3}) \cdot 4 \sqrt{3}
\][/tex]
Step 3: Combine the constants and the square roots.
[tex]\[
= 2 \cdot 4 \cdot (\sqrt{3} \cdot \sqrt{3})
\][/tex]
Step 4: Since [tex]\(\sqrt{3} \cdot \sqrt{3} = 3\)[/tex],
[tex]\[
= 2 \cdot 4 \cdot 3
\][/tex]
Step 5: Multiply the constants.
[tex]\[
= 8 \cdot 3 = 24
\][/tex]
Therefore, the simplified form of the expression is 24.
So, the correct answer is:
24
