I have been working out for my abbs. the only thing that is hurting is my lower back why is that? isn't it suppose to be my abbs?am i doing it wrong?

Check your form: The abdominal muscles do wrap around to the back and if your form is not correct you can strain your back. Get someone who knows what they are doing (trainer etc) to watch you.

Likely yes: You should feel it in your abdomen not your back. Your form likely has an error. Unfortunately, cannot explain how to do the range of ab-exercises correctly in 400 characters--need observed by an experienced partner / trainer / coach to see where your technique needs adjusted.

Partial crunches: ( half sit up) works the abs. The last part of a full crunch uses the back muscles. You may be working the back muscles with the abs.