I'm not so sure about how grammatically correct this sentence is. It is widely used colloquially though. Generally, the structure is אותו ה for masculine singular, אותה ה for feminine singular, אותם ה for masculine plural and אותן ה for feminine plural.
So a correct sentence would be יש לי את אותם המכנסיים, with the את being added in order to avoid being too literary and unnatural.
An inflected form of את + the definite article ה means "the same". So if the את indicates the direct object of a sentence, it must come either in its original form plus a noun with the definite article, or simply in its inflected form alone.
For example: I saw the man - ראיתי את האיש
I saw him - ראיתי אותו (the את is inflected)
I saw the same man - ראיתי את אותו האיש (the first את indicates the direct object, the second, inflected one, together with the article, means "the same".)
No, to say "I have their pants" I think it would be: יש לי את המיכנסיים שלהם
Though this is the very first introduction of אותם as meaning "the same" and it is not mentioned in the unit notes.
Course authors, if you are reading: ambushing learners like this isn't helpful - it's discouraging and frustrating.