1.
\[ 3a(2 - 3b) - (3a - 2b) = \] \[ =6a - 9ab - 3a + 2b= \] \[ = 3a - 9ab + 2b \]

2.
\[ -x^{2} + x(2x + 3) + 2(3x^{2} - 4x) = \] \[ = -x^{2} + 2x^{2} + 3x + 6x^{2} - 8x = \] \[ = 7x^{2} - 5x \]

3.
\[ (2a - 1)(3a + 2) = \] \[ = 6a^{2} + 4a - 3a - 2 = \] \[ = 6a^{2} + a - 2 \]

4.
\[ (4x - 2)(-3x + 2) = \] \[ = -12x^{2} + 8x + 6x - 4 = \] \[ = -12x^{2} + 14x - 4 \]

5.
\[ 1\frac{1}{2}(2b - 4) - \frac{2}{3}(3 - 6b) = \] \[ = \frac{3}{2}(2b - 4) - \frac{2}{3}(3 - 6b) = \] \[ = 3b - 6 - 2 + 4b = \] \[ = 7b - 8 \]

6.
\[ \left(1\frac{2}{3}x + \frac{1}{2}\right)(6 - 12x) + 6x - \frac{1}{4} = \] \[ = \left(\frac{5}{3}x \cdot 6 - \frac{5}{3}x \cdot 12x + \frac{1}{2} \cdot 6 - \frac{1}{2} \cdot 12x\right) + 6x - \frac{1}{4} = \] \[ = 10x - 20x^{2} + 3 - 6x + 6x - \frac{1}{4} = \] \[ = -20x^{2} + 10x + \left(3 - \frac{1}{4}\right) = \] \[ = -20x^{2} + 10x + \frac{11}{4} \]