Cosa pensi di . . . = What do you think about . . .
Cosa pensi di me = What do you think about me
Cosa pensi di questo = What do you think about this
Cosa pensi di fare = What are you going to do
dimostrare = to demonstrate / show / prove
Cosa pensi di demonstrare = What do you think you are proving
It doesn't mean "you're". You are now learning that two languages often express the same concept in different ways. Italian says pensi di [infinitive of verb] - literally "you think of [to verb]" - whereas we say "you think you are [verb]ing".
Remember pensare di [verb] as one pattern, not separate words. Pensa di dimostrare would be S/he thinks s/he is proving.
@MichaelWat Yes it is, according to https://www.thesaurus.com/browse/prove.
Perhaps you mean that they are not always interchangeable, which is true for most words.
Translating poses a permanent challenge, which is to choose the right synonym for the context. See for example all the possible contexts at https://dizionari.repubblica.it/Italiano-Inglese/D/dimostrare.html. As we are not given a context here, we have no idea which, and hope that Duo allows several sensible ones (some hope!).
I hate to disagree....but if you are thinking about something someone or somewhere etc..you must use pensare a not pensare di...which is usually followed by an infinitive... Che Cosa ne pensi = What do you think about... Cosa pensi A me = What do you think about me Cosa ne pensi di questo = What do you think about (of) this. Cosa pensi di fare = What are you thinking of doing. But.. What are you going to do = Cosa faraì. Short explanation Pensare A = Think About Pensare Di = Think of.
Below are the definition and examples from the Hoepli dictionary. All of its choices suit our phrase, and to them I'd add "have in mind" to reflect the context avere in animo.
See http://dizionari.repubblica.it/Italiano-Inglese/P/pensare.php, context #5.
V+di+INF (= progettare/avere in animo) to plan, to think [of doing], to intend Pensava di partire per una lunga vacanza = he intended to leave for a long holiday. Cosa pensi di fare? = what are you planning to do? Pensi di comprarlo? = are you thinking of buying it? Stanno pensando di prendersi una vacanza il mese prossimo = they're thinking of taking a holiday next month.
Note that this only applies to pensare di +infinitivo, not to pensare a or pensare alone.
And I wrote "What are you thinking of demonstrating" and also got it right. Both of our answers are very close to a literal translation and not difficult to come up with. I suspect that the people who want to translate pensare as hope or plan are making this more difficult than it needs to be.
We use the same words in Swedish to express this meaning. "Vad tänker du (göra?)" means "What are you going to (do?)", but uses the word "tänker" = "think". I suspect it is the same in Italian and think therefore that the DL translation is misleading in this case. Please correct me if not.
Note for DL - how come the answer in the discussion group page is completely different from the answer on the questions page? This is shown as "what do you plan to show" This aspect of inconsistency the keeps cropping up on DL makes it more difficult to follow the thread for learning