Step 1: Understanding the Concept
The figure shows a six-membered saturated ring (cyclohexane). One ring carbon carries a \(\text{CH}_3\text{O}\) group (methoxy). The carbon on the opposite side of the ring carries two ethyl groups, drawn as two two-carbon chains.
Step 2: Key Formula or Approach
Ethers are named as alkoxy-alkanes. The ring is the parent. Number the ring so that the substituents get the lowest locants, then write the names alphabetically.
Step 3: Locants
The two ethyl groups sit on one carbon and the methoxy is on the carbon directly across the ring (position 4 from it). Numbering from the diethyl carbon gives locants 1,1,4. Numbering from the methoxy carbon gives 1,4,4. The set 1,1,4 is lower at the first point of difference.
Step 4: Alphabetical order
"Diethyl" is alphabetised under e and "methoxy" under m, so ethyl comes first.
\[ \text{1,1-diethyl-4-methoxycyclohexane} \]
Step 5: Eliminate others
Options (B) and (C) say dimethyl, but the groups drawn have two carbons each. Option (D) numbers from the wrong carbon.
Final Answer:
The compound is 1,1-diethyl-4-methoxycyclohexane, option (A).
\[ \boxed{\text{1,1-diethyl-4-methoxycyclohexane}} \]
