Step 1: Understanding the Question:
The reaction sequence involves two steps: first, the Birch reduction of anisole (methoxybenzene) to form product X, followed by a carbene addition reaction with $\text{CHBr}_3$ and $\text{EtONa}$ to form product Y.
Step 2: Detailed Explanation:
In the first step, methoxybenzene (anisole) undergoes Birch reduction using sodium in liquid ammonia ($\text{Na, liq. }\text{NH}_3$) in the presence of ethanol ($\text{EtOH}$).
Since the methoxy group ($-\text{OCH}_3$) is an electron-donating group (via resonance, $+\text{M}$ effect), it directs the reduction to the 2,5-positions of the ring, keeping the carbon attached to the $-\text{OCH}_3$ group unreduced.
This yields 1-methoxycyclohexa-1,4-diene as the product X.
In the second step, product X is treated with bromoform ($\text{CHBr}_3$) and sodium ethoxide ($\text{EtONa}$).
This reagent combination generates dibromocarbene ($:\text{CBr}_2$) in situ via $\alpha$-elimination.
Dibromocarbene is an electrophilic carbene and selectively adds to the more electron-rich double bond of 1-methoxycyclohexa-1,4-diene.
The double bond bearing the methoxy group ($-\text{OCH}_3$) is significantly more electron-rich than the other isolated double bond due to the strong $+\text{M}$ effect of the methoxy oxygen.
Therefore, the addition of the carbene occurs exclusively at the $\text{C}=\text{C}$ double bond containing the $-\text{OCH}_3$ group to form a fused dibromocyclopropane ring.
This yields the bicyclic product Y, which is 1,1-dibromo-2-methoxybicyclo[4.1.0]hept-3-ene.
Comparing with the options, option (A) correctly represents the structures of X and Y.
Step 3: Final Answer:
The correct option is (A).