Tip: See my list of the Most Common Mistakes in English. It will teach you how to avoid mistakes with commas, prepositions, irregular verbs, and much more (PDF Version).
First, let me note that “homework” is an uncountable (mass) noun in English. It is a common mistake, even among some non-native teachers of English as a foreign language, to say things like, “Hand in your homeworks, please.” The word “homework”, being uncountable, does not have a plural form. If you really must refer to several separate “pieces” of homework, the word you are looking for is “assignment”:
You will get two separate homework assignments today. (correct)
You will get two separate homeworks today. (wrong)
It is also not possible to use “homework” with “a”:
Do you have homework? (correct)
Do you have any homework? (correct)
Do you have a homework? (wrong)
Let’s move on to the main topic of this article. Without further ado, the correct verb to use with “homework” is “do”, not “make”:
I did my homework yesterday. (correct)
I made my homework yesterday. (wrong)
“Homework” is not in any way special in this respect. We always use “do” with activities and “make” with objects that are being made. Just like we “do work”, not “make work”, we also “do homework”, meaning the activity.
The confusion arises from the fact that the most direct translation of “homework” into other languages often refers to the sheets of paper on which the assignments are written, hence it would make sense to “make it”. For the very same reason, we wouldn’t usually speak about “writing homework”:
I have to do my homework now. (correct)
I have to write my homework now. (unnatural)
Наверное, я должен был обратить на это внимание, но тот тип показался мне настоящим психом. Беккер нахмурился. Слова Стратмора эхом звучали в его ушах. Мне нужно все, что было у Танкадо при .