1. **State the problem:** We need to expand and simplify the expression $$3(x - 2)(2x + 3)$$ and write it in the form $$Ax^2 + Bx + C$$ to find the values of $$A$$, $$B$$, and $$C$$. 2. **Recall the distributive property and FOIL method:** To multiply two binomials, we use the FOIL method (First, Outer, Inner, Last). 3. **Multiply the binomials:** $$(x - 2)(2x + 3) = x \cdot 2x + x \cdot 3 - 2 \cdot 2x - 2 \cdot 3$$ $$= 2x^2 + 3x - 4x - 6$$ $$= 2x^2 - x - 6$$ 4. **Multiply the result by 3:** $$3(2x^2 - x - 6) = 3 \cdot 2x^2 - 3 \cdot x - 3 \cdot 6$$ $$= 6x^2 - 3x - 18$$ 5. **Identify coefficients:** $$A = 6, \quad B = -3, \quad C = -18$$ **Final answer:** $$A = 6, \quad B = -3, \quad C = -18$$