Multiply the coefficient 4 of the first term
by the coefficient 9 of the last term, getting 36.

Write down all the ways to factor 36 into 
the product of two integers:

36*1=36
18*2=36
12*3=36
 9*4=36
 6*6=36

Since the sign of the last term  is +,
let's add the same numbers (if the last sign
were negative we would subtract them)

36*1=36, 36+1=37
18*2=36, 18+3=21
12*3=36, 12+3=15
 9*4=36,  9+4=36
 6*6=36,  6+6=12

Now look among those sums for the coefficient
(in absolute value) of the middle term.  The
coefficient of the middle term is -12, and
there is a 12 on the bottom line of the sums
above, which I colored red, so replace 12 in 
the middle term -12xy by the (6+6) which
appears just before the 12 above:

-12xy
-(6+6)xy
reverse the factors so you can distribute easier:
-xy(6+6)
Distribute:
-6xy-6xy

[Notice that you could have just skipped straight
from -12xy to -6xy-6xy in just one step!  I just
went through that to explain why it works]

Now replace the middle term -12xy in



by the two terms -6xy-6xy



Factor 2x out of the first two terms



Factor  out of the last two terms,
remembering that when you take the
negative factor  out of the positive
term,  you get a negative, .



Notice that you have a common binomial factor.
I will color it red in both:



Now you can take out that red binomial factor
the same way as you take out factors that have only
one term.  You write the red binomial factor first, 
and then put the two remaining black factors in a 
parentheses after them.



Now since those just happen to be the same binomial
factor we write it as just one of them squared:



Edwin