What does Pickering offer to do in Pygmalion?

Act Two of 's
opens on Colonel Pickering and Professor Henry Higgins reviewing the vowel
sounds they both can pronounce in Higgin's home laboratory on Wimpole Street. They are surprised
when Liza, the flower girl who they had encountered in Covent Garden the previous day, arrives
at Higgin's home and insists to his housekeeper that she needs to speak with him. When given the
opportunity to do so, Liza informs Higgins that she would like to pay him for speech lessons so
that she can learn to "talk more genteel" and eventually obtain a position as a lady
in a flower shop.

Both Liza and Colonel Pickering are enchanted by Higgin's
earlier claim that in the space of three months, he could provide enough polishing to Liza's
English to pass her off as a duchess at an ambassador's garden party. Impressed by Higgin's
phonetic skills and research, but desiring to see him actively at work, Colonel Pickering
creates a wager with him: Pickering offers to cover all of the expenses of the
"experiment" and to pay for Liza's speech lessons if Higgins can successfully do as he
bragged he could do and pass Liza off as a duchess at the ambassador's garden party. This,
Colonel Pickering claims, would make Higgins "the greatest teacher alive." 

Higgins agrees to these terms, stating, "Yes: in six months--in three if she has a
good ear and a quick tongue--I'll take her anywhere and pass her off as
anything."