$\frac{6 a b - b^{2} + 12 a c - 2 b c}{b + 2 c}$ .

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Solution

$\frac{6 a b - b^{2} + 12 a c - 2 b c}{b + 2 c} = \frac{6 a (b + c) - b (b + 2 c)}{b + 2 c} = \frac{(6 a - b) (b + 2 c)}{(b + 2 c)} = (6 a - b)$

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