$$\frac{ 2-(1-4x) }{ 4 } - \frac{ 4-3x }{ 8 } = \frac{ 3x-1 }{ 2 } - \frac{ 2(3x-4) }{ 6 }$$
$x = \frac{26}{21} = 1\frac{5}{21} \approx 1.238095238$
$$6\left(2-\left(1-4x\right)\right)-3\left(4-3x\right)=12\left(3x-1\right)-4\times 2\left(3x-4\right)$$
$$6\left(2-1-\left(-4x\right)\right)-3\left(4-3x\right)=12\left(3x-1\right)-4\times 2\left(3x-4\right)$$
$$6\left(2-1+4x\right)-3\left(4-3x\right)=12\left(3x-1\right)-4\times 2\left(3x-4\right)$$
$$6\left(1+4x\right)-3\left(4-3x\right)=12\left(3x-1\right)-4\times 2\left(3x-4\right)$$
$$6+24x-3\left(4-3x\right)=12\left(3x-1\right)-4\times 2\left(3x-4\right)$$
$$6+24x-12+9x=12\left(3x-1\right)-4\times 2\left(3x-4\right)$$
$$-6+24x+9x=12\left(3x-1\right)-4\times 2\left(3x-4\right)$$
$$-6+33x=12\left(3x-1\right)-4\times 2\left(3x-4\right)$$
$$-6+33x=36x-12-4\times 2\left(3x-4\right)$$
$$-6+33x=36x-12-8\left(3x-4\right)$$
$$-6+33x=36x-12-24x+32$$
$$-6+33x=12x-12+32$$
$$-6+33x=12x+20$$
$$-6+33x-12x=20$$
$$-6+21x=20$$
$$21x=20+6$$
$$21x=26$$
$$x=\frac{26}{21}$$
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