The LCR reaction of Benzene and Methane to form Dimethylbenzene is incorrect, it should be Benzene + 2 Methane -> Dimethylbenzene + 4 Hydrogen.
Alternatively, we could potentially do the methylation properly with something like dimethyl sulfate

Also, there was a short discussion regarding positional isomers of Xylene (dimethylbenzene) and its role in Diphenyl Isophthalate, starting here https://discord.com/channels/701354865217110096/701354865657643070/940288471669547008. Gonna put it here in case anyone wants to deal with it