Question 155849
The wording of the problem is not very clear but I'll try to tackle it as I understand it. Here it is rewritten into legible and (hopefully) equivalent form.

{{{sqrt(3)/(2*sqrt(6))}}}
{{{2 = sqrt(4)}}}
{{{sqrt(4)*sqrt(6) = sqrt(24)}}}
{{{sqrt(3)/sqrt(24) = sqrt(3/24) = sqrt(1/8) = 1/sqrt(8)}}} //*{{{sqrt(2)}}}
{{{sqrt(2) / (sqrt(2) * sqrt(8)) = sqrt(2)/sqrt(16) = sqrt(2)/4}}}
(it's usually good to get rid of the fractions in the denominator) 

I am using two basic laws of radicals, that:
a) {{{sqrt(a) * sqrt(b) = sqrt(a*b)}}}
b) {{{sqrt(a)/sqrt(b) = sqrt(a/b)}}}

Cheers,
Adam