To multiply the polynomials \((x - 6)\) and \((4x + 3)\), you need to use the distributive property, often referred to in this context as the FOIL method (First, Outer, Inner, Last). Here’s a step-by-step breakdown:
1. First: Multiply the first terms in each binomial.
[tex]\[
x \cdot 4x = 4x^2
\][/tex]
2. Outer: Multiply the outer terms.
[tex]\[
x \cdot 3 = 3x
\][/tex]
3. Inner: Multiply the inner terms.
[tex]\[
-6 \cdot 4x = -24x
\][/tex]
4. Last: Multiply the last terms in each binomial.
[tex]\[
-6 \cdot 3 = -18
\][/tex]
Next, we add all of these results together:
[tex]\[
4x^2 + 3x - 24x - 18
\][/tex]
Now, combine the like terms (\(3x\) and \(-24x\)):
[tex]\[
4x^2 - 21x - 18
\][/tex]
So, the result of multiplying \((x - 6)\) and \((4x + 3)\) is:
[tex]\[
4x^2 - 21x - 18
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{C. \, 4x^2 - 21x - 18}
\][/tex]
