Conventions of Composition Rule 77 Practice
I insist that you "take care" of your younger siblings when your parents go out.
"Take care" should NOT be in quotation marks because quotation marks aren't for emphasis. The sentence makes sense without any quotation marks. If the person is joking about doing something silly with the siblings, something that's not really taking care of them, then the quotation marks can stay.
He was the "only" person in the room who understood why the quadratic formula works.
"Only" should not be in quotation marks if the person being talked about is indeed the only person in the room who understands this formula. If everyone in the room understands, one could keep the quotation marks.
They kept saying they "needed" to have that new book when what they meant was that they "wanted" it.
The word "needed" can stay in quotation marks, but the word "wanted" should not have quotation marks around it.
Employees must "wash hands" before returning to work.
There should not be quotation marks in this sentence. Employees handling food should actually wash their hands, and with the quotation marks, the sentence implies that they should say they're washing their hands without actually washing them. Yikes!