\(6\left(9x^4-16+15x^3-20x\right):\left(3x^2-4\right)\\ =6\left[\left(9x^4-16\right)+\left(15x^3-20x\right)\right]:\left(3x^2-4\right)\\ =6\left[\left(3x^2-4\right)\left(3x^2+4\right)+5x\left(3x^2-4\right)\right]:\left(3x^2-4\right)\\ =6\left(3x^2-4\right)\left(3x^2+4+5x\right):\left(3x^2-4\right)\\ =6\left(3x^2+5x+4\right)\\ =18x^2+30x+24\)