I was going to test fit the tein basic dampers, but only the rear. If I keep the front stock, what will happen to the ride?

 

Can you be more vague? What are you expecting to happen? I don't understand this test fit stuff. Put them all on of leave them all off-front and back. They're meant to be installed as a set.

 

^He likely bought coilovers that aren't for his car, and is worried about the fitment.

Or he wants to adjust the height?

That is just a guess though.

Depending if the basic is shorter then the OE shock ( doubt it, but possible) the car will be lower.

Chances are the will be lower in the rear, and the coilovers will have a impact on the ride quality, becuase the spring rates are siffer then stock.