These girls seem to be Abigail and Brittany Hensel, born in 1990.
I'm not sure though if this TLC is a TV channel or just a show. I found several web pages that mentioned them when I googled their names. I'll assume that Abigail and Brittany are indeed the twins in question.
Brittany and Abigail Hensel are dicephalic parapagus twins: they have separate organs--lungs, heart, stomach, spine, and each has complete control over her own arm--until their bodies meet at the pelvis.
Because of the arrangement of their bodies, the procedure to separate them as babies would have been way too risky.
I remember watching a documentary about Abby and Brittany Hensel a few years ago--they were young teenagers at the time, just learning how to drive.