Multiply the polynomials \((3x^{2} - 2x + 1)\) and \((4x^{2} + 3x - 2)\)

Step 1 ：First, distribute each term of the first polynomial to each term of the second polynomial. This gives: \(3x^{2} * 4x^{2} + 3x^{2} * 3x + 3x^{2} * -2 + -2x * 4x^{2} + -2x * 3x + -2x * -2 + 1* 4x^{2} + 1*3x + 1*-2\)

Step 2 ：Then, simplify each individual term to get: \(12x^{4} + 9x^{3} - 6x^{2} - 8x^{3} - 6x^{2} + 4x + 4x^{2} + 3x - 2\)

Step 3 ：Finally, combine like terms to get: \(12x^{4} + x^{3} - 8x^{2} + 7x - 2\)