We multiply the polynomials using the rule $a^m\cdot a^n = a^{m+n}$ to guide us. $$\begin{aligned} \left({-5a^{5}}\right)\left({6a^{10}-9a^{10}b^{9}+4b^{6}}\right)&= -30a^{5+10}+45a^{5+10}b^{9} - 20a^{5}b^{6}\\ & = {-30a^{15}+45a^{15}b^{9}-20a^{5}b^{6}} \end{aligned}$$ Note that we are using the distributive property of multiplication in this problem: $x(y+z)=xy+xz$.