Answer:
y
Step-by-step explanation:
((((2•3y3) -  22y2) -  3y) -  —) -  2
                                y     
STEP
4
:
Rewriting the whole as an Equivalent Fraction
 4.1   Subtracting a fraction from a whole
Rewrite the whole as a fraction using  y  as the denominator :
                       6y3 - 4y2 - 3y     (6y3 - 4y2 - 3y) • y
     6y3 - 4y2 - 3y =  ——————————————  =  ————————————————————
                             1                     y          
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
STEP
5
:
Pulling out like terms
 5.1     Pull out like factors :
   6y3 - 4y2 - 3y  =   y • (6y2 - 4y - 3) 
Trying to factor by splitting the middle term
 5.2     Factoring  6y2 - 4y - 3 
The first term is,  6y2  its coefficient is  6 .
The middle term is,  -4y  its coefficient is  -4 .
The last term, "the constant", is  -3 
Step-1 : Multiply the coefficient of the first term by the constant   6 • -3 = -18 
Step-2 : Find two factors of  -18  whose sum equals the coefficient of the middle term, which is   -4 .
      -18    +    1    =    -17	
      -9    +    2    =    -7	
      -6    +    3    =    -3	
      -3    +    6    =    3	
      -2    +    9    =    7	
      -1    +    18    =    17	
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Adding fractions that have a common denominator :
 5.3       Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
 y • (6y2-4y-3) • y - (6)     6y4 - 4y3 - 3y2 - 6 
 ————————————————————————  =  ———————————————————
            y                          y         
Equation at the end of step
5
:
  (6y4 - 4y3 - 3y2 - 6)     
  ————————————————————— -  2
            y              
STEP
6
:
Rewriting the whole as an Equivalent Fraction :
 6.1   Subtracting a whole from a fraction
Rewrite the whole as a fraction using  y  as the denominator :
         2     2 • y
    2 =  —  =  —————
         1       y  
Checking for a perfect cube :
 6.2    6y4 - 4y3 - 3y2 - 6  is not a perfect cube
Trying to factor by pulling out :
 6.3      Factoring:  6y4 - 4y3 - 3y2 - 6 
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1:  -3y2 - 6 
Group 2:  6y4 - 4y3 
Pull out from each group separately :
Group 1:   (y2 + 2) • (-3)
Group 2:   (3y - 2) • (2y3)
Bad news !! Factoring by pulling out fails :
The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
 6.4    Find roots (zeroes) of :       F(y) = 6y4 - 4y3 - 3y2 - 6
Polynomial Roots Calculator is a set of methods aimed at finding values of  y  for which   F(y)=0  
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  y  which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient
In this case, the Leading Coefficient is  6  and the Trailing Constant is  -6.
 The factor(s) are:
of the Leading Coefficient :  1,2 ,3 ,6
 of the Trailing Constant :  1 ,2 ,3 ,6
 Let us test ....
  	P    Q    P/Q    F(P/Q)    	Divisor
      -1       1        -1.00        1.00    	
      -1       2        -0.50        -5.88    	
      -1       3        -0.33        -6.11    	
      -1       6        -0.17        -6.06    	
      -2       1        -2.00        110.00    	
Note - For tidiness, printing of 13 checks which found no root was suppressed
Polynomial Roots Calculator found no rational roots
Adding fractions that have a common denominator :
 6.5       Adding up the two equivalent fractions
 (6y4-4y3-3y2-6) - (2 • y)      6y4 - 4y3 - 3y2 - 2y - 6 
 —————————————————————————  =  ————————————————————————
             y                            y            
Polynomial Roots Calculator :
 6.6    Find roots (zeroes) of :       F(y) = 6y4 - 4y3 - 3y2 - 2y - 6
     See theory in step 6.4
In this case, the Leading Coefficient is  6  and the Trailing Constant is  -6.
 The factor(s) are:
of the Leading Coefficient :  1,2 ,3 ,6
 of the Trailing Constant :  1 ,2 ,3 ,6
 Let us test ....
  	P    Q    P/Q    F(P/Q)    	Divisor
      -1       1        -1.00        3.00    	
      -1       2        -0.50        -4.88    	
      -1       3        -0.33        -5.44    	
      -1       6        -0.17        -5.73    	
      -2       1        -2.00        114.00    	
Note - For tidiness, printing of 13 checks which found no root was suppressed
Polynomial Roots Calculator found no rational roots
Final result :
  6y4 - 4y3 - 3y2 - 2y - 6 
  ————————————————————————
             y