1. The problem is to find the product of $6x$ and the polynomial $(x^2 - 4x - 3)$. 2. The formula used here is the distributive property: $a(b + c + d) = ab + ac + ad$. 3. Apply the distributive property: $$6x(x^2 - 4x - 3) = 6x \cdot x^2 - 6x \cdot 4x - 6x \cdot 3$$ 4. Multiply each term: $$6x \cdot x^2 = 6x^{3}$$ $$6x \cdot 4x = 24x^{2}$$ $$6x \cdot 3 = 18x$$ 5. Substitute back: $$6x^{3} - 24x^{2} - 18x$$ 6. This is the final expanded form of the product. Answer: $$6x^{3} - 24x^{2} - 18x$$