What is the correct $IUPAC$ name of the following structure? Explain.
$CH_3-CH_2-CH(CH_2-CH_3)-CH_2-CH_2-CH(CH_3)-CH_2-CH_3$
$(i)$ $3-$ethyl$-6-$methyloctane
$(ii)$ $3-$methyl$-6-$ethyloctane
$(iii)$ $6-$methyl$-3-$ethyloctane

(A) $1$. Identify the longest carbon chain: The longest chain contains $8$ carbon atoms,so the parent alkane is octane.
$2$. Number the chain: Numbering from left to right gives substituents at positions $3$ (ethyl) and $6$ (methyl). Numbering from right to left gives substituents at positions $3$ (methyl) and $6$ (ethyl). Both sets of locants are $(3, 6)$.
$3$. Apply alphabetical order: When locant sets are the same,the substituent that comes first alphabetically receives the lower number. Since 'ethyl' comes before 'methyl',the ethyl group is assigned position $3$ and the methyl group is assigned position $6$.
$4$. Conclusion: The correct name is $3-$ethyl$-6-$methyloctane. Therefore,option $(i)$ is correct.