1. **State the problem:** Multiply the polynomials $ (x + 6)(x - 2) $ and simplify the result. 2. **Formula used:** To multiply two binomials, use the distributive property (also known as FOIL method): $$ (a + b)(c + d) = ac + ad + bc + bd $$ 3. **Apply the formula:** $$ (x + 6)(x - 2) = x \cdot x + x \cdot (-2) + 6 \cdot x + 6 \cdot (-2) $$ 4. **Calculate each term:** $$ = x^2 - 2x + 6x - 12 $$ 5. **Combine like terms:** $$ -2x + 6x = 4x $$ 6. **Final simplified expression:** $$ x^2 + 4x - 12 $$ This is the product of the two polynomials, fully simplified.