她的办公室离这里近 should be accepted
So the 很 is mandatory?
Actually we don't say that in real life. We just say 她的辦公室在附近. It is exactly the same English meaning for "Her offive is close to here." In my opinion, the English sentence is not accurate. I am a Chinese, I just clicked this for fun. Lol
Is it ungrammatical without离?
Yeah, that character means the location of the place before it is being compared to the place after it.
The hints need to be more helpful