Step 1: Approach
Read the structure, count carbons in each branch, then build the name.
Step 2: Reading the picture
Ring: 6 carbons, so cyclohexane. Left branch: $\text{CH}_3\text{-O-}$, which is methoxy. Right branch: two lines each ending in a bend, which are two ethyl groups on the same carbon.
Step 3: Numbering
Number the ring starting at the carbon with the two ethyl groups as $1$. Both ethyls are at position 1 and the methoxy is at position 4, so the locant set is $\{1,1,4\}$. The alternative start gives $\{1,4,4\}$, which is higher.
Step 4: Name
\[ \text{1,1-diethyl-4-methoxycyclohexane} \]
This is option (A). Names containing "dimethyl" do not fit because the alkyl groups are ethyl.
Final Answer:
The compound is 1,1-diethyl-4-methoxycyclohexane, option (A).
\[ \boxed{\text{1,1-diethyl-4-methoxycyclohexane}} \]