Answer:
(Mechanism in attachment).
Explanation:
The Williamson ether synthesis is the most used method to form ethers, in which an alkoxide ion reacts with a primary alkyl halide in an SN₂ reaction. Usually, the alkoxide ion is prepared by the reaction of an alcohol with a strong base like sodium hydride, NaH.
The alkyl halide must be primary so an attack by the backside is not impeded. When the alkyl halide is not primary, the result is usually an elimination.
Mechanism
Step 1: form the alkoxide of the alcohol considering the most impeded group (in this case, the 4-methoxyphenol).
Step 2: the alkoxide displaces the leaving group from a good SN₂ substrate (the propyl bromide).
Therefore, in Williamson ether synthesis, the alkyl halide must be a good SN₂ substrate (generally primary). We choose the alkyl group less impeded to be the halide and the most impeded group to be the alkoxide ion.