Final answer:
TFIIIB is the complex made up of Brf, B" and TBP, and it plays a critical role in forming the transcription initiation complex necessary for the synthesis of mRNA in eukaryotic cells.
Step-by-step explanation:
The complex in question, comprised of Brf, B" and TATA-binding protein (TBP), is TFIIIB. During the initiation phase of transcription in eukaryotes, multiple transcription factors are required to recruit RNA polymerase II to the promoter of a protein-coding gene. Among these, TFIIIB is part of a larger group of basal transcription factors, each denoted by 'TFII' followed by a specific letter. TFIIIB is essential in the recruitment and assembling of transcription factors and polymerase to form the transcription initiation complex, allowing it to start synthesizing mRNA.