Step 1: Recall IUPAC naming rules.
To name a compound we find the longest carbon chain, give the lowest locant numbers, list substituents in alphabetical order, and name the main functional group with the correct suffix.
Step 2: Find the parent chain of X.
The longest continuous chain in X has $7$ carbons, so the parent is heptane.
Step 3: Place the substituents on X.
X carries an ethyl group at carbon $4$ and a methyl group at carbon $3$, after numbering from the end that gives the lowest locants. Listing alphabetically (ethyl before methyl) gives \[ 4\text{-ethyl-3-methylheptane}. \]
Step 4: Find the parent chain of Y.
Y has an $-OH$ group, which gets suffix priority. The longest chain holding the $OH$ has $4$ carbons, so the parent is butan-2-ol.
Step 5: Place the phenyl group on Y.
A phenyl group sits on carbon $1$, so the name is \[ 1\text{-phenylbutan-2-ol}. \]
Step 6: Match to the option.
The pair $4$-ethyl-3-methylheptane and $1$-phenylbutan-2-ol matches one option exactly. \[ \boxed{\text{4-ethyl-3-methylheptane ; 1-phenylbutan-2-ol}} \]