a)
\frac{12}{3-\sqrt3}=\frac{12*(3+\sqrt3)}{(3-\sqrt3)(3+\sqrt3)}=\frac{12(3+\sqrt3)}{9-3}=\frac{12(3+\sqrt3)}{6}=2(3+\sqrt3)
b)
\frac{2\sqrt3}{2+\sqrt6}=\frac{2\sqrt3*(2-\sqrt6)}{(2+\sqrt6)(2-\sqrt6)}=\frac{4\sqrt3-2\sqrt{18}}{4-6}=\frac{4\sqrt3-2\sqrt{9*2}}{-2}=\frac{4\sqrt3-2*3\sqrt2}{-2}=
=-2\sqrt3+3\sqrt2=3\sqrt2-2\sqrt3