There really are not any examples where the society in The Giver violates the Third Amendment to the Constitution of the United States. The society in the book violates many of the other amendments in the Bill of Rights, but it does not seem to violate the Third Amendment.
The Third Amendment to the Constitution of the United States is somewhat obscure. It reads
No Soldier shall, in time of peace be quartered in any house, without the consent of the Owner, nor in time of war, but in a manner to be prescribed by law.
This amendment is not particularly relevant as our government would not do this in modern times. In fact, the Supreme Court has never had to decide a case based on this amendment.
In The Giver, it would be very hard for the society to clearly violate this amendment. As far as we can tell, the society does not have any soldiers. We know that they do not know about war because Jonas is overwhelmed by the memory of war that the Giver gives to him in Chapter 15. They may have some sort of military since the jet in Chapter 1 sounds like a fighter airplane, but we never actually see any discussion of soldiers in the text. If the society does not have soldiers (or if they are not discussed) we cannot find any clear violations of the Third Amendment.
I suppose that you could try to say that the society violates the Third Amendment by assigning people to live together as families, but even that does not really work for me. In order to get a spouse, you have to ask for one, which means that you consent to have that person live with you. The same applies if you want to have children live with you. Since the people have to give their consent, this would not violate the Third Amendment, even if we were to say that the Third Amendment does not apply only to soldiers.
Because of this, I do not think there are any violations of the Third Amendment in this book. Other amendments, like the 1st, 4th, and 5th appear to be violated, but not the Third.