[tex]\displaystyle\\
\sqrt{12}\times\left(\sqrt{108}-2\sqrt{48}\right)=\\\\
=\sqrt{4\times 3}\times\left(\sqrt{36\times 3}-2\sqrt{16\times 3}\right)=\\\\
=2\sqrt{3}\times\left(6\sqrt{3}-2\times4\sqrt{3}\right)=\\\\
=2\sqrt{3}\times\left(6\sqrt{3}-8\sqrt{3}\right)=\\\\
=2\sqrt{3}\times\left(-2\sqrt{3}\right)=-4\times 3 = \boxed{\bf -12}
[/tex]
