解:
先化简$2A-B$:
$\begin{aligned}&2A-B=&2(x^2+xy+2y-12)-(2x^2-2xy+x-1)\\=&2x^2+2xy+4y-24-2x^2+2xy-x+1\\=&4xy+4y-x-23\end{aligned}$
(1) 当$x=-1,y=-2$时,代入化简后的式子:
$\begin{aligned}&2A-B=&4×(-1)×(-2)+4×(-2)-(-1)-23\\=&8-8+1-23\\=&-22\end{aligned}$
(2) 合并含$x$的项,整理得:
$2A-B=(4y-1)x +4y -23$
因为$2A-B$的值与$x$的取值无关,所以$x$的系数为0,即:
$4y-1=0$
解得:
$y=\dfrac{1}{4}$