"They do not see your shoes."
Translation:Senin ayakkabını görmüyorlar.
Why is 'sizin' ['your' 2nd person plural/formal] not accepted?
As you say, sizin just means "your", not "They do not see your shoes."
You will have to type more words than just that -- for example, Sizin ayakkabınızı görmüyorlar.
What was your entire answer?
Did you perhaps use the wrong possessive suffix on "shoes"?
But it looks from your answer that I should have used 'ayakkabınızı'
That is correct.
although I do not know why!
Because the possessive ending has to match the owner:
- benim ayakkabım
- senin ayakkabın
- onun ayakkabısı
- bizim ayakkabımız
- sizin ayakkabınız
- onlarin ayakkabısı / ayakkabıları
See https://en.wiktionary.org/wiki/ayakkab%C4%B1 (open up "inflection" and then "possessive forms").
And in this sentence, it's the definite (because it's possessed) object of a verb, so you need the accusative case: add -ı after all forms ending in a consonant, -yı after forms ending in a vowel.
Thus sizin ayakkabınızı.