$a)\left[{\left(2a^2{b}^3\right)}^6\cdot {\left(2a^2{b}^3\right)}^3\right]:\left[{\left(2a^2{b}^3\right)}^2\cdot {\left(2a^2{b}^3\right)}^5\right]=[\left(2^6\cdot a^{2\cdot 6}\cdot b^{3\cdot 6}\right)\cdot \left(2^3\cdot a^{2\cdot 3}\cdot b^{3\cdot 3}\right]:\left[\left(2^2\cdot a^{2\cdot 2}\cdot b^{3\cdot 2}\right)\cdot \left(2^5\cdot a^{2\cdot 5}\cdot b^{3\cdot 5}\right)\right]=\left[2^6\cdot a^{12}\cdot b^{18}\cdot 2^3\cdot a^6\cdot b^9\right]:\left[2^2\cdot a^4\cdot b^6\cdot 2^5\cdot a^{10}\cdot b^{15}\right]=$

$\left[2^{6+3}{a}^{12+6}{b}^{18+9}\right]:\left[2^{2+5}{a}^{4+10}{b}^{6+15}\right]=2^9\cdot a^{18}\cdot b^{27}:2^7\cdot a^{14}\cdot b^{21}=2^{9-7}\cdot a^{18-14}\cdot b^{27-21}=2^2\cdot a^4\cdot b^6=4\cdot a^4\cdot b^6$ $\left[2^{6+3}{a}^{12+6}{b}^{18+9}\right]:\left[2^{2+5}{a}^{4+10}{b}^{6+15}\right]=2^9\cdot a^{18}\cdot b^{27}:2^7\cdot a^{14}\cdot b^{21}=2^{9-7}\cdot a^{18-14}\cdot b^{27-21}=2^2\cdot a^4\cdot b^6=4\cdot a^4\cdot b^6$

$a=-6,b=-\frac{1}{3}$

$4\cdot a^4\cdot b^6=4\cdot {\left(-6\right)}^4\cdot {\left(-\frac{1}{3}\right)}^6=4\cdot {\left(-1\right)}^4\cdot 6^4\cdot {\left(-1\right)}^6\cdot {\left(\frac{1}{3}\right)}^6=4\cdot 6^4\cdot {\left(\frac{1}{3}\right)}^6=4\cdot 6^4\cdot {\left(\frac{1}{3}\right)}^4\cdot {\left(\frac{1}{3}\right)}^2=4\cdot {\left(6\cdot \frac{1}{3}\right)}^4\cdot {\left(\frac{1}{3}\right)}^2=4\cdot {\left(\frac{6}{3}\right)}^4\cdot \frac{1}{9}=4\cdot 2^4\cdot \frac{1}{9}=4\cdot 16\cdot \frac{1}{9}=\frac{64}{9}=7\frac{1}{9}$

$b)\frac{2\cdot {\left(x^{12}:x^5\cdot x^3\right)}^4-5\cdot {\left(x^{12}\cdot x^{12}:x^4\right)}^2}{6\cdot {\left(x^2\cdot x^3\cdot x^2\cdot x^{11}:x^9\right)}^4}=\frac{2\cdot {\left(x^{12-5+3}\right)}^4-5\cdot {\left(x^{12+12-4}\right)}^2}{6\cdot {\left(x^{2+3+2+11-9}\right)}^4}=\frac{2\cdot {\left(x^{10}\right)}^4-5\cdot {\left(x^{20}\right)}^2}{6\cdot {\left(x^9\right)}^4}=\frac{2\cdot x^{40}-5\cdot x^{40}}{6\cdot x^{36}}=(x^{40}\cdot \frac{2-5}{6\cdot x^{36}}=\frac{-3\cdot x^{40}}{6\cdot x^{36}}=\frac{-3\cdot x^{36}\cdot x^4}{6\cdot x^{36}}=\frac{-x^4}{2}$

$x=-0,2$

$\frac{-x^4}{2}=\frac{-{\left(-0,2\right)}^4}{2}=-\frac{0,04\cdot 0,04}{2}=-\frac{0,0016}{2}=-0,0008$