In CKKS, we only support the CRT/Evaluation encoding (you can go to coefficient encoding using the SlotsToCoef subroutine in CKKS bootstrapping). The coefficient encoding is natively supported in BGV/BFV (along with CRT encoding).
You are asking about doing a multiplication in the coefficient encoding and then doing extraction. Extraction can be done by homomorphically switching to the CRT encoding (expensive) and then doing a masked multiplication or using LWE extraction. Extracting coefficients (via LWE) in the coefficient encoding can be done using automorphisms (a subroutine for this is implemented as part of CKKS scheme switching) - this is cheaper.
At a high level, these are advanced operations that require FHE expertise.