Answer
$3-4\sqrt[3]{63}$
Work Step by Step
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the given expression is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[3]{3}(\sqrt[3]{9}-4\sqrt[3]{21})
\\\\=
\sqrt[3]{3}(\sqrt[3]{9})+\sqrt[3]{3}(-4\sqrt[3]{21})
.\end{array}
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\sqrt[3]{3}(\sqrt[3]{9})+\sqrt[3]{3}(-4\sqrt[3]{21})
\\\\=
\sqrt[3]{3(9)}-4\sqrt[3]{3(21)}
\\\\=
\sqrt[3]{27}-4\sqrt[3]{63}
.\end{array}
Extracting the root of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt[3]{27}-4\sqrt[3]{63}
\\\\=
\sqrt[3]{(3)^3}-4\sqrt[3]{63}
\\\\=
3-4\sqrt[3]{63}
.\end{array}
