Yes. It is esterification
wrong, the reaction of a carboxyl acid with thionyl chloride is not an esterfication, since you do not generate an ester but an acyl chloride
as given by molecular formula C8H6O2
Since when can we tell reactions by there molecular formula?
Your answer is correct since SOCl2 is used to convert carboxyl group COOH into CO2SOCl.
Wrong your carboxyl acid will by converted to acyl chloride R-COCl.
With elimination of HCl, SO2, ester is formed
HCl and SO2 are indeed eliminated, but this will not yield an ester. There could be an ester generated since there is an secondary alcohol present in your molecule and that one can react with the generated acyl chloride.
A secondary alcohol is less reactive so that is why you need to generate an acyl chloride in order for this reaction to occur.
But still its not called a fischer esterfication, since you would then make an ester from a R-COOH and R-OH. Which in this case doesn't happen.