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

$=8-4\sqrt{5}+12\sqrt{5}-6\cdot \sqrt{5}\cdot \sqrt{5}=8-4\sqrt{5}+12\sqrt{5}-6\cdot 5=$  

$=8+8\sqrt{5}-30=8\sqrt{5}-22$