[tex]x+y=-2 \sqrt{3} \\ x^{2} - y^{2} =4 \sqrt{6} \\ x^{2} - y^{2} =(x+y)(x-y) \\ 4 \sqrt{6} =-2 \sqrt3} (x-y) \\ (x-y)= \frac{4 \sqrt{6} }{-2 \sqrt{3} } \\ (x-y)=- \frac{2 \sqrt{6} }{ \sqrt{3}} \\ (x-y)=- \frac{2 \sqrt{6} \sqrt{3} }{3} \\ (x-y)=- \frac{6 \sqrt{2} }{3} \\ (x-y)=-2 \sqrt{2} [/tex]
