Final answer:
The eukaryotic post-transcriptional modification that enhances mRNA stability and translational efficiency is 5'-capping, where a 7-methylguanosine cap is added to the pre-mRNA.
Step-by-step explanation:
The type of eukaryotic post-transcriptional modification that enhances both stability and translational efficiency is A) 5'-Capping. This process involves the enzymatic addition of a 7-methylguanosine cap to the 5' end of the nascent pre-messenger RNA (pre-mRNA) as it is being synthesized. This cap protects the mRNA from degradation and is recognized by factors involved in protein synthesis, aiding in the initiation of translation by ribosomes. Another important post-transcriptional modification is B) Polyadenylation, which adds a poly-A tail to the pre-mRNA's 3' end, further protecting it from degradation and signaling for export to the cytoplasm.