Sodium Hydroxide = NaOH, this is used to neutralise the HCl, simple Acid/Base reaction.
That your teacher has given you this question assumes that you know how to write an equation for this and do titration calculations to calculate the number of moles of HCl.
After that point, the rest is just simple moles calculations that you should be able to work through pretty easily.
Fundamentally this is not to difficult a question. Break it down, take it slow, and know your equations.
no moles = mass/Mr
concentration = no moles / volume (dm3)
1000cm3 = 1dm3
As i said, if you have issues, show us the calculations you have done which will allow us to work out where you went wrong. The obvious step which would give you an"astronomical" Ar would be to miss that the HCl has been made up to 250cm3 of which only 25cm3 has been titrated with NaOH. Otherwise you are either using the wrong equations or messed up the working.
The answer gives you an atom which does have the ability to covalently bond to 4 Chlorine atoms. There aren't many of those. Bit of an oddity actually, but that's by the by.