how to work with Quotient rings

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In this extension $\frac{\mathbb Q[x]}{<6+4x+6x^2+3x^3>}:\mathbb Q$,is this $-3x^3=6+4x+6x^2$ true?

Also is this like a general rule?

where can I find specific topics about this? and for example not just working with $\mathbb Q[x]$ but with $\mathbb Z_5[x] $ or another weird rings like the first one?

Apologies for my ignorance in abstract algebra..