[tex]12x\sqrt{\cfrac{3}{2}}~~ = ~~6\sqrt{3}\implies (6)(2)x\cdot \cfrac{\sqrt{3}}{\sqrt{2}}~~ = ~~6\sqrt{3}\implies \cfrac{(2x)(6\sqrt{3})}{\sqrt{2}}=6\sqrt{3} \\\\\\ \cfrac{2x}{\sqrt{2}}=\cfrac{6\sqrt{3}}{6\sqrt{3}}\implies \cfrac{2x}{\sqrt{2}}=1\implies 2x=\sqrt{2}\implies x=\cfrac{\sqrt{2}}{2}[/tex]
