Answer:
A) I intend is the correct answer.
Explanation:
D) I would Intend would be grammatically incorrect.
If you substitute each possible answer into the subject which makes more sense?
The receptionist asked me how long I would intend to stay. (Wrong)
The receptionist asked me how long I intended to stay (Almost right)
The receptionist asked me how long I had intended to stay. (Very Wrong)
or
The receptionist asked me how long I intend to stay. (Right!)
Look at the hints in the text to know which is grammatically correct.
The receptionist asked (Past tense) me how long ___________ to stay (Present tense.)
With this info we can tell the correct answer is option A, I intend.