\[(a - 4b)\left( a^{2} + 3ab - 6b^{2} \right) =\]
\[= a^{3} - 4a^{2}b + 3a^{2}b - 12ab^{2} - 6ab^{2} + 24b^{3} =\]
\[= a^{3} - a^{2}b - 18ab^{2} + 24b^{3}.\]