Change the sign of the  in  to 

Start with this

3 | 2 -8  -4  -6
  |   
   -------------

Bring down the 2    

3 | 2 -8  -4  -6
  |    
   -------------
    2 

Multiply the 2 by the 3, getting 6.
Then write it above and to the right
of the 2:


3 | 2 -8  -4  -6
  |    6  
   -------------
    2 

Combine the -8 and the 6, getting -2 and
write it at the bottom:

3 | 2 -8  -4  -6
  |    6  
   -------------
    2 -2 

Multiply the -2 by the 3, getting -6.
Then write it above and to the right
of the -2:


3 | 2 -8  -4  -6
  |    6  -6 
   -------------
    2 -2 

Combine the -4 and the -6, getting -10 and
write it at the bottom:

3 | 2 -8  -4  -6
  |    6  -6 
   -------------
    2 -2 -10 

Multiply the -10 by the 3, getting -30.
Then write it above and to the right
of the -10:


3 | 2 -8  -4  -6
  |    6  -6 -30
   -------------
    2 -2 -10 

Combine the -6 and the -30, getting -36 and
write it at the bottom:

3 | 2 -8  -4  -6
  |    6  -6 -30
   -------------
    2 -2 -10 -36

Now we interpret that bottom line of numbers:
The largest power of x in the original numerator
 is 3.  So subtract one from
3 and get 2 for the exponent of x.  So the first
three numbers on the bottom is to be interpreted 
as

  

Then the last number, -36, is the remainder and
we put that over the original divisor 
and this fraction is added to the quotient:

  

Now we can just write that as MINUS that fraction:

   

Edwin