Sooo confuseddd🤷

Somebody please explain to me or help me understand this. So today we had our first prenatal appoinment and our due date was November 23rd, 2019 by the health dept. Due my last period was February 20th, 2019. I would be right at 9 weeks today. So today we go to our appointment they do the checkup then an ultrasound and come in amd say im 6.5 weeks due December 12th, 2019 (or somewhere around there). Being 6.5 weeks ago would be 3 weeks after the day i tested. Which i waited the whole term my period was due then tested the next day. So therefore i would have been 2-3 weeks pregnant and i have heard that when your 6 weeks pregnant its 6 weeks from last day of last period. Im missing 2.5-3 weeks.. When did i concieve? Am i really 6.5 weeks? How can this happen?

Sorry the doctor didnt explain anything to us. She told us how far along and then walked out.