Answer:
2*sqrt2
Explanation:
In right isosceles triangles, the ratios of the sides are: 
1:1:sqrt(2) 
1=the legs, and sqrt2 being the hypotenuse. 
So, in this problem, we can simply divide the hypotenuse by sqrt2 to find the legs. 
2*sqrt6/sqrt2=2*sqrt3 
Therefore, the lengths of the legs are 2*sqrt2