"The man does not find his trousers."
Translation:Người đàn ông không tìm thấy quần của mình.
But how do you know if it's past action or not? In this case they use the present tense - does not find. Use of thấy in this sentence to me would mean he hasn't found them yet, implying that he's been looking a long time. They should translate it better if they want to teach us when it's proper to use thấy.
"tìm thấy" is the result of "tìm". you tìm sthg when you don't know where it is, and you stop tìm when you tìm thấy (sometimes shortened to "thấy") it.
in our case here, if you leave out "thấy", you are saying that the man does not look for his pants (at some point, implying that he just does not care where they are)