​ Please help, ty!

This type is a little tricky, RP......

When the divisor  is in the linear form    ax + b     [ or  ma + b, in this case ....since  "a" is the variable ] we need to be careful about the residual polynomial...the remainder will be correct, however

Set  6a + 8  = 0   ⇒   a  =  -4/3....this is what we need to divide by

-4/3  [ 6     - 4   - 76       - 44    - 6      - 63   ]

                 -8      16         80     -48       72   

       _______________________________

         6    -12     - 60        36    -54         9

The correct remainder is 9

Here is where synthetic division fails to produce the correct residual polynomial.....the resulting polynomial  appears  to be :

6a^4 - 12 a^3  - 60a^2  + 36a  -  54

However....note that if we  performed the "normal" polynomial division....the first term would be......a^4

                 a^4

6a + 8   [ 6a^5

              -(6a^5)   ......

So...this means that we need to divide every co-efficient of the apparent residual polynomial by 6  to get the correct answer

So...the residual polynomial is

a^4  - 2a^3  - 10a^2  + 6a  - 9  R [ 9/ (6a + 8) ] 

Do you see this  ??