I know the tert is a strong non-nucleophillic base and is known to be used in dehydrohalogenation reactions but I dont see how a F would be removed. Ive been toying with the mw as a first step to solving this. Adding a carbon would result in mw of 288. Its probably easier than it looks and its possibly just me and my lack of sleep.
This is displacement of the para F and the ortho F with methoxide, these are the 2 compounds with mass 288.
The other is displacement with ethoxide, probably the para F, to give a compound with mass 302.
Methoxide gives the ortho displacement probably due to less steric crowding.
Perhaps you can work out the mechanism?