This site shows maps of extant formations from the different epochs. The Palo Pinto Mountains are from the Carboniferous Period, also known as Pennsylvanian.
This next map shows the now almost eroded Oachita Mountain range that formed around the same time as the Palo Pinto Mountains did, maybe from the same contintental squeezing during pangea around 300 million years ago. The Oachita Mountains eventually sank with the Ft. Worth basin. West Texas maintained its altitudinal sedementary plains as water drained through the rivers and creeks of the Palo Pinto Mountains to the sea.