"How are you, professor? Really well."
Translation:Ciamar a tha sibh, ollaimh? Tha gu dòigheil.
This has not been fully explained yet. But this is not a fault - it is because they are trying to keep things simple to start with.
To keep things very simple - since all will be revealed in due course - all verbs in almost all tenses in Gaelic have two forms: one for when there is no preceding word (tha) and one for when there is a preceding word (chan eil).
Usually the two words would be very similar, but all languages have oddities and this is one in Gaelic. Firstly, eil is a 'suppletive' form. Like go becoming went in English it is just an irregular form. There is a historical explanation but we won't go there now (for eil or for went!). The second problem is that we say chan eil and nach eil but a bheil. This is caused by eil having been *feil. How that led to the present situation is best left as it is to with the different mutations caused by an in Irish and cha in Gaelic.
If you think it is hard learning two, or occasionally three, forms for a verb remember that Gaelic and its sisters Irish and Manx are the only ones out of all our neighbours (including our first cousins like Welsh) where you do not have to learn all the forms I am, you are, she is, we are etc. so Gaelic actually has it pretty easy.
Thu is informal and used with someone you know well (in a friendly sense). It's also singular and you use it when speaking to someone younger.
Sibh is used when someone is in a position of respect. Older people, parents, teachers, doctors, war veterans, etc. It's also the plural form, for example "how are you guys?" in English.
Do they accept just "Gu dòigheil" as the answer to the question here? That's how I wrote it the first time, and I got it wrong. But then I noticed that I had a typo in "ciamar" - I put a 'u' instead of the 'i'. So I don't know if they marked it wrong for the tupo, or for leaving out "tha" in "tha gu dòigheil".