[tex]a)2 \sqrt{3} \times 4 \sqrt{6} = 8 \sqrt{18} = 2 \sqrt{2} [/tex]
[tex]b)2 \sqrt{3} \times ( - \sqrt{2}) = - 2 \sqrt{6} [/tex]
[tex]c) \frac{ - 2 \sqrt{2} }{3} \times \frac{ \sqrt{2} }{4} = - \frac{ \sqrt{2} }{3} \times \frac{ \sqrt{2} }{2} = - \frac{2}{6} = - \frac{1}{3} [/tex]
[tex]d)( - 2 \sqrt{3}) \times ( - \frac{ \sqrt{3} }{2}) = 2 \sqrt{3} \times \frac{ \sqrt{3} }{2} = 3[/tex]
[tex]e) - 4 \sqrt{3} \times \sqrt{7} = - 4 \sqrt{2 \times 7} = - 4 \sqrt{21} [/tex]
[tex]f)6 \sqrt{5} \times ( - \frac{ \sqrt{5} }{30} )= 6 \sqrt{5} + \frac{ \sqrt{5} }{30} = \frac{181 \sqrt{5} }{30} [/tex]