(6x^2 + x + 3)x(5x^2 + 2) in Z_10 =

6x-2-x-3-x-5x-2-2-in-z-10-a-x-3-2x-6-b-5x-3

(6x^2 + x + 3)x(5x^2 + 2) in Z_10 =
A. x^3 + 2x + 6
B. 5x^3 + 7x^2 + 2x + 6
C. x^3 + 7x^2 + 2x + 6
D. None of the mentioned
Correct option is B. 5x^3 + 7x^2 + 2x + 6

(6x^2 + x + 3)x(5x^2 + 2) in Z_10 =  5x^3 + 7x^2 + 2x + 6.
We can find this via basic polynomial arithmetic in Z_10.