jmc

Begin by distributing in the innermost parentheses: $$\begin{array}{rl}\left(2x+\frac{3}{2}(4x-6)\right)-& 4\left(-(2-x)+\frac{x}{2}\right)\\ & =(2x+6x-9)-4\left(-2+x+\frac{x}{2}\right)\\ & =(8x-9)-4\left(-2+\frac{3x}{2}\right)\end{array}$$ Now, distribute again, and combine like terms: $$\begin{array}{rl}(8x-9)-4\left(-2+\frac{3x}{2}\right)& =8x-9+8-6x\\ & =\boxed{2x-1}\end{array}$$