Answer
$-7a\sqrt[3]{3a}$
Work Step by Step
Using the properties of radicals, then,
\begin{array}{l}
2\sqrt[3]{3a^4}-3a\sqrt[3]{81a}
\\=
2\sqrt[3]{a^3\cdot3a}-3a\sqrt[3]{27\cdot3a}
\\=
2\cdot a\sqrt[3]{3a}-3a\cdot3\sqrt[3]{3a}
\\=
2a\sqrt[3]{3a}-9a\sqrt[3]{3a}
\\=
-7a\sqrt[3]{3a}
.\end{array}