$\displaystyle \begin{array}{{>{\displaystyle}l}} \sqrt{\left( 2\sqrt{3} -3\sqrt{2}\right)^{2}} +\sqrt{13-4\sqrt{3}} -\sqrt{22+12\sqrt{2}}\\ =|2\sqrt{3} -3\sqrt{2} |+\sqrt{12-2.2\sqrt{3} +1} -\sqrt{18+2.2.3\sqrt{2} +4}\\ =3\sqrt{2} -2\sqrt{3} +\sqrt{\left( 2\sqrt{3} -1\right)^{2}} -\sqrt{\left( 3\sqrt{2} +2\right)^{2}}\\ =3\sqrt{2} -2\sqrt{3} +|2\sqrt{3} -1|-|3\sqrt{2} +2|\\ =3\sqrt{2} -2\sqrt{3} +2\sqrt{3} -1-3\sqrt{2} -2\\ =-3 \end{array}$
