Step 1: Recall the rule for who's, whose, who, and whom.
"Who's" is short for "who is" or "who has." "Whose" shows possession, asking who something belongs to. "Who" works as the subject of a verb. "Whom" works as the object of a verb or preposition.
Step 2: Check option A, "Who's car are you planning to borrow?"
This sentence asks about ownership of a car, so it needs the possessive word "whose," not the short form "who's" (who is). The underlined word is wrong here.
Step 3: Check option B, "Whose planning to have a birthday party?"
This sentence really asks "who is planning," so it needs "who's," not "whose." The underlined word is wrong here too.
Step 4: Check option C, "He is the person who you met at the junction."
Here "you met" the person, so the person is the object of "met." An object needs "whom," not "who." The underlined word is wrong.
Step 5: Check option D, "Does he know whom to call about the hotel reservations?"
Here the person is being called, so the person is the object of "to call." An object correctly takes "whom" here, and that is exactly the underlined word used.
Final Answer:
Only option D uses its underlined word correctly, so option D is correct. \[ \boxed{\text{Option D}} \]