$$6(1 \times 2-1 \times 1)-2(4 \times 2-1 \times 4)+3(4 \times 1-1 \times 4)$$
$-2$
$$6\left(2-1\times 1\right)-2\left(4\times 2-1\times 4\right)+3\left(4\times 1-1\times 4\right)$$
$$6\left(2-1\right)-2\left(4\times 2-1\times 4\right)+3\left(4\times 1-1\times 4\right)$$
$$6\times 1-2\left(4\times 2-1\times 4\right)+3\left(4\times 1-1\times 4\right)$$
$$6-2\left(4\times 2-1\times 4\right)+3\left(4\times 1-1\times 4\right)$$
$$6-2\left(8-1\times 4\right)+3\left(4\times 1-1\times 4\right)$$
$$6-2\left(8-4\right)+3\left(4\times 1-1\times 4\right)$$
$$6-2\times 4+3\left(4\times 1-1\times 4\right)$$
$$6-8+3\left(4\times 1-1\times 4\right)$$
$$-2+3\left(4\times 1-1\times 4\right)$$
$$-2+3\left(4-1\times 4\right)$$
$$-2+3\left(4-4\right)$$
$$-2+3\times 0$$
$$-2+0$$
$$-2$$
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