The answer is:
besoin de
Explanation:
This sentence translates as:
Sorry/Apologies, I cannot go out, I need (I have the need) to tidy my room.
The other options were:
dois - have to
This couldn't have been used here as it makes no sense for it to follow the verb 'avoir' in its current state, unless modified - resulting in another tense or simply excluded.
peux - can
suis - (I) am from 'etre' which means 'to be'
