Cardinality of the quotient ring $\mathbb{Z}[x]/(x^2-3,2x+4)$

Cardinality of the quotient ring $\mathbb{Z}[x]/(x^2-3,2x+4)$

This problem is from a practice exam I was working on.
What is the cardinality of the quotient $\mathbb{Z}[x]/(x^2-3,2x+4)$ ?
Thoughts. If I find a ring that is easier to handle then this then I can
go from there. So I think this is isomorphic to
$\mathbb{Z}_2[x]/(x^2-3,x+2)$. And then I am stuck.
Am I correct so far? What should I be looking to do from here?
Thanks for your time and your answers.