ithink this will do...

take this LHS...

(sqrt(6) - sqrt(2))/ 4

taking square

we get,

= (6+2-2sqrt(12))/16

= (8-2sqrt(12))/16

taking 2 out, and cancelling we get,

= (4-sqrt(12))/8

= (4 -(sqrt(3)*sqrt(4)))/8 sqrt(4) = 2

taking 2 out side and cancelling with denominator we get,

= (2-sqrt(3))/4

taking sqrt now we get,

=sqrt(2-sqrt(3))/2 = answer.