$\text{a)}$  

$\sqrt{3}\cdot \left(3\sqrt{24}-4\sqrt{6}+5\sqrt{54}\right)=\sqrt{3}\cdot \left(3\sqrt{4\cdot 6}-4\sqrt{6}+5\sqrt{9\cdot 6}\right)=$

$=\sqrt{3}\cdot \left(3\cdot 2\sqrt{6}-4\sqrt{6}+5\cdot 3\sqrt{6}\right)=\sqrt{3}\cdot \left(6\sqrt{6}-4\sqrt{6}+15\sqrt{6}\right)=$

$\sqrt{3}\cdot 17\sqrt{6}=17\sqrt{3\cdot 6}=17\sqrt{18}=17\sqrt{9\cdot 2}=17\cdot 3\sqrt{2}=51\sqrt{2}$

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$\text{b)}$  

$\sqrt{10}\cdot \left(2\sqrt{20}-7\sqrt{8}-4\sqrt{5}-2\sqrt{18}\right)=\sqrt{10}\cdot \left(2\sqrt{4\cdot 5}-7\sqrt{4\cdot 2}-4\sqrt{5}-2\sqrt{9\cdot 2}\right)=$

$=\sqrt{10}\cdot \left(2\cdot 2\sqrt{5}-7\cdot 2\sqrt{2}-4\sqrt{5}-2\cdot 3\sqrt{2}\right)=\sqrt{10}\cdot \left(4\sqrt{5}-14\sqrt{2}-4\sqrt{5}-6\sqrt{2}\right)=$   

$=\sqrt{10}\cdot \left(-20\sqrt{2}\right)=-20\sqrt{10\cdot 2}=-20\sqrt{20}=-20\sqrt{4\cdot 5}=-20\cdot 2\sqrt{5}=-40\sqrt{5}$