a)
[tex]\bf 3\sqrt{2}\cdot 4\sqrt{3}= \boxed{\bf 12\sqrt{6} }[/tex]
b)
[tex]\bf -2\sqrt{7}\cdot 5\sqrt{2}= \boxed{\bf -10\sqrt{14} }[/tex]
c)
[tex]\bf 6\sqrt{6}\cdot \sqrt{5}= \boxed{\bf 6\sqrt{30} }[/tex]
d)
[tex]\bf 12\sqrt{6}:(4\sqrt{3})=\boxed{\bf 3\sqrt{2} }[/tex]
e)
[tex]\bf 30\sqrt{14}:(-5\sqrt{2})=\boxed{\bf -6\sqrt{7} }[/tex]
f)
[tex]\bf 8\sqrt{18}:\sqrt{6}= \boxed{\bf 8\sqrt{3} }[/tex]