P → Q. Excess CHX3MgBr adds twice to the ester, giving the tertiary alcohol Ar−CHX2CHX2C(OH)(CHX3)X2, with Ar = 4-tert-butylphenyl.
Q → R. Cold HX2SOX4 gives the tertiary cation, which attacks the ring ortho to the side chain (intramolecular Friedel-Crafts alkylation). This closes a five-membered ring: R is 6-tert-butyl-1,1-dimethylindane.
R → S. Friedel-Crafts acylation with CHX3COCl/AlClX3 goes to the free ring position that is ortho to the ring CHX2 and meta to tert-butyl (C-4). The other positions are hindered by tert-butyl or by the gem-dimethyl group.
S is 4-acetyl-6-tert-butyl-1,1-dimethylindane: structure (A).
(A)