1. **State the problem:** Simplify the expression $\left(x-6\right)\left(x+3\right)$. 2. **Recall the distributive property (FOIL method):** When multiplying two binomials, multiply each term in the first binomial by each term in the second binomial. 3. **Apply FOIL:** $$\left(x-6\right)\left(x+3\right) = x \cdot x + x \cdot 3 - 6 \cdot x - 6 \cdot 3$$ 4. **Calculate each term:** $$= x^2 + 3x - 6x - 18$$ 5. **Combine like terms:** $$= x^2 - 3x - 18$$ 6. **Final answer:** The simplified form of $\left(x-6\right)\left(x+3\right)$ is $$x^2 - 3x - 18$$