I believe it isn’t. In Polish it is very common to write “Ty”, “Twój”, “Wy”, “Wasz” etc. starting with capital in letters, emails and other forms of correspondence to show politeness to the recipient and everything connected to him.
The capital letter is not necessary and the sentence is perfectly fine with “twojego”, but many Poles would write it with capital, because they are taught to write every second person pronoun with a capital.
Well, frankly, it shouldn't be capitalized here. This is a sentence taken out of context (like every single sentence in Duolingo), like a line of dialogue in a book, and therefore "twojego" shouldn't be capitalized.
But if you were writing this very sentence as a text message to someone, it should be capitalized. You are then addressing someone directly and thus such politeness is recommended.
I wouldn’t say it ‘should be’. It could, and it is pretty common, but I for one do not really like the custom and never do it, so I always write twój, ty etc. in private correspondence, except for the beginning of the sentence. It depends on the recipient of your writing.
You should capitalize second person pronouns in more official correspondence – if you write to an office, a company, a university professor, etc. it could be considered impolite if not capitalized.