The first step is nucleophilic substitution.

It is possible for nucleophile to attack directly at the allylic position, displacing the leaving group in a single step, in a process referred to as $\mathrm{S_N2'}$ substitution. This is likely in cases when the allyl compound is unhindered, and a strong nucleophile is used. The products will be similar to those seen with $\mathrm{S_N1'}$ substitution. Thus reaction of 1-chloro-2-butene with sodium hydroxide gives a mixture of 2-buten-1-ol and 3-buten-2-ol:

Step 1: Williamson Ether synthesis

• para-Cresol reacts with 3,3-dimethylallylbromide to give 1 and 2 using potassium carbonate in acetone as shown below.

Step 2: 3,3-Sigmatropic rearrangement (Aromatic Claisen rearrangement)

• Compounds 1 and 2 undergo 3,3-sigmatropic rearrangement (Aromatic Claisen rearrangement)${^1}$. Compound 1 gives 3 via sigmatropic shift followed by tautomerism to give 4 (as shown below).

Similarly, 2 gives 5 via sigmatropic shift followed by tautomerism to give 6 (as shown below).

Net reaction

As per the question given, the following is the scheme.

References

${^1}$:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3873100/${^2}$:https://chem.libretexts.org/Bookshelves/Organic_Chemistry/Map%3A_Organic_Chemistry_(McMurry)/Chapter_18%3A_Ethers_and_Epoxides%3B_Thiols_and_Sulfides/18.04_Reactions_of_Ethers_-_Claisen_Rearrangement

${^3}$:J. Am. Chem. Soc.19891112511-519 Publication Date:January 1, 1989https://doi.org/10.1021/ja00184a018