Answer
$-\sqrt[3]{4}+2\sqrt[3]{2}$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL method, then,
\begin{array}{l}
\left( \sqrt[3]{4}+2 \right)\left( \sqrt[3]{2}-1 \right)
\\=
(\sqrt[3]{4})(\sqrt[3]{2})+(\sqrt[3]{4})(-1)+(2)(\sqrt[3]{2})+(2)(-1)
\\=
\sqrt[3]{8}-\sqrt[3]{4}+2\sqrt[3]{2}-2
\\=
2-\sqrt[3]{4}+2\sqrt[3]{2}-2
\\=
-\sqrt[3]{4}+2\sqrt[3]{2}
.\end{array}