When you divide polynomials, you can use long division to find the answer.
The step by step process is:
As the remainder is -8, the result of the division is:
[tex]x-2+\frac{-8}{(3x-2)}=x-2-\frac{8}{3x-2}[/tex]
Then A in terms of x is:
[tex]\begin{gathered} A-\frac{8}{3x-2}=(x-2)-\frac{8}{3x-2} \\ \text{Then} \\ A=x-2 \end{gathered}[/tex]
