I get up to the starred part and then break down the square root but the answer I get isn't the one in the book. The book tells me the answer is
3 plus or minus the square root of 6 over 3
Your working is good until you get to the point where you try to divide out the 6's...that is an invalid move. Try dividing everything in the numerator and denominator by 2, since 2 is a factor of both the numerator and denominator.