Help me understand the car sell game

So I have a car that’s upside down by 12k and the value is 20k. I thought if I get a bigger vehicle that I want for ($27k) I can use my car value ($20k) put towards the car ($27k) I would finance the rest meaning ($20k) after taxes and negative total. I guess it doesn’t work that way. They give you the value of the car ($20k) which leaves ($7k) that plus dealer tag and taxes will be added to your whole balance of ($32k) making everything ($40k). Is this correct?