Read every arrow as "which chemical does this job?" and match it to the standard reagent.
Step 1: Swapping OH for Cl on an alcohol is a substitution of the hydroxyl group. Thionyl chloride is preferred because it leaves no liquid impurity: \(R\text{-}OH + SOCl_2 \rightarrow R\text{-}Cl + SO_2 + HCl\). (Phosphorus chlorides PCl5/PCl3, or Lucas reagent conc. HCl + ZnCl2, are acceptable too.)
Step 2: To install Br in place of OH, use phosphorus and bromine, which generate PBr3: \(3R\text{-}OH + PBr_3 \rightarrow 3R\text{-}Br + H_3PO_3\). So the blank is P + Br2 (i.e. PBr3).
Step 3: Turning a symmetrical alkene into a vicinal dihalide (Br on each of the two carbons) is simple electrophilic addition of molecular bromine: \(CH_2{=}CH_2 + Br_2 \rightarrow BrCH_2CH_2Br\). Reagent = Br2 in CCl4.
Step 4: Here Br lands on the CH2 that is far from the ring (the less substituted carbon). Markovnikov addition of HBr would put Br on the benzylic carbon; to reverse the selectivity we add a peroxide, which switches the mechanism to free radicals. Reagent = HBr in the presence of a peroxide (Kharasch/peroxide effect): \(C_6H_5CH{=}CH_2 + HBr \xrightarrow{\text{peroxide}} C_6H_5CH_2CH_2Br\).
Reagents: (i) SOCl2, (ii) PBr3, (iii) Br2, (iv) HBr + peroxide.