Which sentence is correct: 창문을 닫아주십시오 or 창문을 닫어주십시오?
The Korean language has vowel harmony. A letter which contains ㅏ, ㅗ, ㅑ, ㅛ, ㅘ, ㅚ, ㅐ(positive vowel) is followed by -아. A letter which contains ㅓ, ㅜ, ㅕ, ㅠ, ㅔ, ㅝ, ㅟ, ㅖ (negative vowel) is followed by -어.
For example, 닫 contains a positive vowel ㅏ, so you have to use 아 after the letter. In contrast, 먹 has a negative vowel ㅓ, it is followed by 어.
FYI) But there are many exceptions in Korean. Furthermore, vowel harmony is continuously vanishing from modern Korean. It is always recommended to check dictionaries first.
One thing that may trip a new learner is: even though 닫아주십시오 is absolutely correct as a written form, when speaking, Koreans frequently pronounce it as 닫어주십시오. Just like an English speaker would write "Going to be there" and pronounce it as "Gonna be there".
In general, if a verb/adjective ends with ㅏ+(consonant)+-다 (such as 닫다, 잡다, 막다, 안다), then it can be pronounced with -어 in colloquial speech.
Of course, there's a good chance that your textbook will say "닫아 is correct and 닫어 is wrong!", which is, well, true in the sense that it's standard - so always remember to spell it as 닫아, and it's probably a good idea to pronounce it as 닫아 as well, but when someone else pronounces it as 닫어, now you know what it means.