Using your knowledge of activators and repressors, hypothesize two ways in which transcription of the lct gene could be turned off.

One hypothesis would be that there are allosteric repressors that bind to RNA-polymerase and change its conformation. This way, it's unable to bind to the promoter for lct gene.
Another hypothesis would be that the repressors bind to a silencer or operator sequence of the lct gene. This prevents transcription of the gene even though the RNA polymerase may be capable of binding to the promoter.

Could you elaborate?

D.) domain, kingdom, phylum, class, order, family, genus then species