$\text{a)}\left(3\sqrt{3}+\sqrt{2}\right)\cdot \sqrt{3}=3\sqrt{3}\cdot \sqrt{3}+\sqrt{2}\cdot \sqrt{3}=3\cdot {\sqrt{3}}^2+\sqrt{2\cdot 3}=$  

$=3\cdot 3+\sqrt{6}=9+\sqrt{6}$  

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$\text{b)}\sqrt{2}\left(1-\sqrt{2}\right)=\sqrt{2}\cdot 1-\sqrt{2}\cdot \sqrt{2}=\sqrt{2}-{\sqrt{2}}^2=\sqrt{2}-2$  

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$\text{c)}\sqrt[3]{7}\cdot \sqrt[3]{7^2}=\sqrt[3]{7\cdot 7^2}=\sqrt[3]{7^3}=7$  

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$\text{d)}\sqrt{2-\sqrt{3}}\cdot \sqrt{\sqrt{3}+2}=\sqrt{\left(2-\sqrt{3}\right)\left(\sqrt{3}+2\right)}=\sqrt{2\cdot \sqrt{3}+2\cdot 2-\sqrt{3}\cdot \sqrt{3}-\sqrt{3}\cdot 2}=$  

$=\sqrt{2\sqrt{3}+4-{\sqrt{3}}^2-2\sqrt{3}}=\sqrt{4-3}=\sqrt{1}=1$