$$x-\frac{2x+8}{3}=\frac{1}{4}(x-\frac{2-x}{6})-3$$
$x=-10$
$$12x-4\left(2x+8\right)=3\left(x-\frac{2-x}{6}\right)-36$$
$$12x-8x-32=3\left(x-\frac{2-x}{6}\right)-36$$
$$4x-32=3\left(x-\frac{2-x}{6}\right)-36$$
$$4x-32=3x+3\left(-\frac{2-x}{6}\right)-36$$
$$4x-32=3x+\frac{2-x}{-2}-36$$
$$4x-32=3x+\frac{-2+x}{2}-36$$
$$4x-32=3x-1+\frac{1}{2}x-36$$
$$4x-32=\frac{7}{2}x-1-36$$
$$4x-32=\frac{7}{2}x-37$$
$$4x-32-\frac{7}{2}x=-37$$
$$\frac{1}{2}x-32=-37$$
$$\frac{1}{2}x=-37+32$$
$$\frac{1}{2}x=-5$$
$$x=-5\times 2$$
$$x=-10$$
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