12. \( \left(-a b^{7}\right)^{2} \cdot\left(12 a^{3} b\right)^{2} \)

To simplify \( \left(-a b^{7}\right)^{2} \cdot\left(12 a^{3} b\right)^{2} \), we start by squaring both parts separately. First, calculate \( \left(-a b^{7}\right)^{2} \): \[ (-a b^{7})^{2} = (-1)^{2} \cdot (a)^{2} \cdot (b^{7})^{2} = 1 \cdot a^{2} \cdot b^{14} = a^{2} b^{14}. \] Next, calculate \( \left(12 a^{3} b\right)^{2} \): \[ (12 a^{3} b)^{2} = 12^{2} \cdot (a^{3})^{2} \cdot (b)^{2} = 144 \cdot a^{6} \cdot b^{2} = 144 a^{6} b^{2}. \] Now, we combine the results: \[ a^{2} b^{14} \cdot 144 a^{6} b^{2} = 144 \cdot a^{2 + 6} \cdot b^{14 + 2} = 144 a^{8} b^{16}. \] Thus, the final simplified expression is: \[ \boxed{144 a^{8} b^{16}}. \]