What about the -6, it looks like it appears from nowhere.  And where is +8x+10? 

Oh I get it now. thanks.

Its the same thing.

take k(x) for example.

h(x) = x or we say the function h(x), graphed as y = x

hence h(k(x)) = k(x) 

Given k(x) = x + 2
we know hk(x) = (x + 2)

formalising an idea,
for an unknown function z(x),
if k(x) is a known function.

and zk(x) can be expressed as y = a + b(k(x)) + c  or a function of k(x), for a,c, are known constants/parameters.
then z(x) is simply  y = a + bx + c

which is how TS, used the "completing the Square method, to obtain the equation as a factor of (k(x))
and work out h(x). An alternative method from inversing the identity.

what method wrong?

Hi . Never knew I'll get so many great responses . Anyway , yes , I finally got to the point that I can't understand the concept from all the reference books available , and also the textbooks . Since I'm currently tuition-less , I'll have to resort to asking on the internet , and I've gotten great responses .

From all of the posts above , I figured I'll simplify the main gist of the concept , at least for me :

We're finding h(x) , but if we map k(x) to the function x^2+8x+10 , I'll get the value of hk(x) instead and not h(x) . And to find x from k(x) , we'll have to inverse it , by letting y as the subject and then from there , express x in terms of y .

Since y is set to be equal to k(x) , which is x+4 , to solve for x , it will be x=y-4 .

But then when it comes to here my logic and reasoning doesn't understand this part : SINCE y=x+4 , and x=y-4 , why do we say its h(y) instead and not h(x) ? Is y=y-4 ?