a: \(3a^2\left(a^2-4a+6\right)=3a^2\cdot a^2-3a^2\cdot4a+3a^2\cdot6\)
\(=3a^4-12a^3+18a^2\)
b: \(\left(2b^2-\dfrac{1}{3}b+4\right)\cdot\left(-\dfrac{3}{6}b^3\right)\)
\(=-\dfrac{1}{2}b^3\left(2b^2-\dfrac{1}{3}b+4\right)=-\dfrac{1}{2}b^3\cdot2b^2+\dfrac{1}{2}b^3\cdot\dfrac{1}{3}b-\dfrac{1}{2}b^3\cdot4\)
\(=-b^5+\dfrac{1}{6}b^4-2b^3\)
________
\(a.3a^2\left(a^2-4a+6\right)\\ =3a^4-12a^3+18a^2\\ b.\left(2b^2-\dfrac{1}{3}b+4\right)\left(-\dfrac{3}{6}b^3\right)\\ =\left(2b^2-\dfrac{1}{3}b+4\right)\left(-\dfrac{1}{2}b^3\right)\\ =-b^5+\dfrac{1}{6}b^4-2b^3\)