Williamson ether synthesis forms an ether by an SN2 reaction between an alkoxide ion and an alkyl halide, so the alkyl halide must be one that accepts backside attack easily. Primary halides work best, secondary are poorer, and tertiary halides fail because steric crowding favours elimination over substitution. To build tert-butyl ethyl ether the bond to form is between the tert-butyl oxygen and the ethyl carbon, so the tertiary fragment must supply the alkoxide and the primary fragment must supply the halide. Sodium tert-butoxide with ethyl bromide satisfies this, since iodide-free primary ethyl bromide undergoes clean SN2. Sodium ethoxide with tert-butyl bromide is wrong because the tertiary halide would mostly eliminate to give isobutylene rather than the ether. The options pairing an alkoxide with a neutral alcohol cannot work because an alcohol is not an electrophilic alkyl halide. This logic is exactly the NCERT guideline for choosing reagents and a standard JEE selection problem. The same reasoning explains why aryl and vinyl halides cannot be used in Williamson synthesis, since their sp2 carbons resist backside SN2 attack, and why secondary halides give reduced yields owing to competing elimination. The alkoxide is typically generated by treating the parent alcohol with sodium metal or sodium hydride beforehand. As a check, always assign the bulky group as the alkoxide and the least hindered group as the halide.