Rationalizing a denominator. The question instructs to rationalize the denominator in the following fraction:

My solution is as follows:

The book's solution is 

which is exactly the numerator in my solution.
Can someone confirm my solution or point what what I'm doing wrong?
Thank you.

Going from the first to the second line of your working, you seem to have said
$$(\sqrt{6} -2)(\sqrt{6}+2) = 6+4$$
on the denominator of the fraction.
This isn't true: in general $(a-b)(a+b)=a^2-b^2$, not $a^2+b^2$.
