What is the $IUPAC$ name of the following compounds?
$(A)$ $CH_3-CH(CH_3)-CH(OH)-CH(C_2H_5)-CH(OH)-CH_3$
$(B)$ $A$ cyclohexane ring with a $-NO_2$ group at position $1$ and a $-OCH_3$ group at position $3$.

(A) The longest carbon chain contains $6$ carbon atoms. The numbering starts from the right to give the lowest locants to the hydroxyl groups. The substituents are an ethyl group at position $3$ and a methyl group at position $5$. Thus,the name is $3$-ethyl-$5$-methylhexane-$2,4$-diol.
$(B)$ The structure is a cyclohexane ring. The methoxy group $(-OCH_3)$ and nitro group $(-NO_2)$ are substituents. Alphabetically,'methoxy' comes before 'nitro'. Numbering the ring to give the lowest locants,we get $1$-methoxy-$3$-nitrocyclohexane.