Final answer:
The abbreviation for the information carrier that transfers genetic information from the nucleus to an organelle for protein production is mRNA, which stands for messenger RNA. option b.
Step-by-step explanation:
The abbreviation that stands for the information carrier from the nucleus to an organelle to produce protein molecules is RNA, specifically messenger RNA (mRNA). Messenger RNA is crucial in the process of protein synthesis as it carries the genetic message from the DNA to the ribosome, the site of protein synthesis. DNA remains in the nucleus, but since protein synthesis occurs in the cytoplasm, mRNA is needed to transfer genetic information through the nuclear pores to the ribosome. This process involves transcription of DNA to mRNA within the nucleus followed by translation, where the mRNA is used by ribosomes to synthesize proteins.