I am trying to identify the following quotient ring using Adding relation method from Artin.

The ring is $\mathbb{Z}[x]/(6,2x-1)$. I did find solution to a similar problem on MSE. Hence I tried to follow the method. Here is my solution:

$2(2x-1)+4=4x-4$. So we get $\mathbb{Z}[x]/(6,4x-4)$ So, lets first kill 6. The ideal (6) is kernel for the homomorphism $\mathbb{Z}[x] \rightarrow \mathbb{Z\_6}$ So, the residue of x is 6. Hence $4x-4=4(6)-4=18$. Therefore the ring is the one which contains 18 elements? Is this correct approach?