Final answer:
The provided excerpts do not relate to Professor Higgins or Eliza's accent from 'Pygmalion', however, in the context of the play, Professor Higgins believes he can teach Eliza to speak with a refined accent and pass her off as a duchess.
Step-by-step explanation:
It appears there is a mix-up with the dialogues provided and the question asked. The given question asks about Professor Higgins and Eliza's accent, which is related to the play 'Pygmalion' by George Bernard Shaw. However, the excerpts provided do not contain any references to Professor Higgins or Eliza, but rather include dialogues from different contexts and possibly different works.
Due to the lack of relevant content in the excerpts regarding Professor Higgins and Eliza, it is difficult to provide an answer to what Professor Higgins said he would be able to do with Eliza's accent.
Nonetheless, for those familiar with the play 'Pygmalion', Professor Higgins is known for boasting that he could transform Eliza's cockney accent and pass her off as a duchess at an ambassador's garden party with elocution lessons, thus reflecting the themes of social mobility and transformation in the play.