Chloe is right.

A is the right answer. as u can see B " so as to" means "in order to" but the question says open the door " quietly"，so B is opposite to what the question mean，and if you choose A , it means " I open the door quietly so I will not wake him up".

In this case b) is correct. A) does not work because the sentence is in past tense but a) is not but if you switched don’t didn’t then you could use a) as well. I hope this helps:)