In Russian 'мой' (also моя and моё) means 'my' and used only when talking about on certain object - Мой кот - my cat Моя тарелка - my plate Моё имя - my name (имя is an exeption, all words ending with -мя are neuter, usually neuter words end with -о, like место (place) or -e like солнце (sun)).
In your sentance мой is masculine singular, but полотенца is neuter plural.
Мои is used with all plural objects asking what? with some exeptions
I wrote this and was told i had a typo, should have been marked as a mistake. Typo should not be an option for multiple choice questions.