"You are showing your watch."
Translation:Pokazujesz twój zegarek.
Why isn't it 'twojego'? Is it 'twój' because of emphasis? This is Accusative isn't it?-the object being what is shown. I still cannot see why twojego cannot be used... Pokazujesz twojego zegarek.
Yes, this is Accusative, Accusative of masculine nouns. That's the only situation where it matters whether the noun is animate or inanimate.
Inanimate masculine nouns have Accusative identical to Nominative. "Pokazujesz [swój/twój] zegarek".
Animate masculine nouns have Accusative identical to Genitive. "Pokazujesz [swojego/twojego] psa".
Besides, "twojego" and "zegarek" don't work together exactly because they have different cases while being parts of one noun phrase. If "twojego" was the right word here, it should also be "zegarka". Like in Genitive-needing sentence "Nie widzę twojego zegarka" (I don't see your watch).
I would accept a sentence like "pokazujesz wasz zegar", because a clock can be an item of furniture that belongs to everyone who lives in the household. But a watch? Rather not.
The problem with your sentence is that it mixes singular "pokazujesz" and plural "wasz", which is of course not wrong (and as you're level 25, I'll assume you did it on purpose), but I wonder if it's safe to accept it because it may confuse many learners.
So for others: This sentence means something like: You, John, are showing your (your wife's and yours) watch.
And well, I agree that a watch is less likely to be owned by more than one person.