I think "quest'orogolio" should be the correct answer, and questo orologio is not OK. Anyone to confirm?
Quest'orologio marked wrong :/ Is there any special rule where it's allowed to put apostrophe between questo and a noun starting on vowel which Duo concerns?
yes, it isn't. "mi piace" = I like. Mi = myself, to me... there's no need to put myself at the end of the sentence
Because "questo orologio" is the subject of the sentence: so the verb must be the 3rd singular person (piace). Mi = a me = "to me" in English
Piacere means "to be pleasing" so "Non piaccio questo orologio" would be sort of like "I am not pleasing, this watch".
So you have to switch it around and say "It's pleasing to me, this watch", which is "Piace a me quest'orologio".
And of course "a me" => "mi" so the most natural translation is "Mi piace quest'orologio".
Having said that, this stupid question doesn't like the abbreviation "quest'orologio" so you have to write "questo orologio".
July 2019 and duolingo still marks you down if you write 'quest'orologio'. Checked with Treccani, and they say that EITHER 'questo orologio' or 'quest' orologio' non è sbagliato.