In Arkansas you are allowed to drive at the age of 14. The state has 3 stages of licenses for teens:
1) Instruction Permit. The purpose of this permit is basically to allow you to learn the rules of the road and other basics, hence; instruction. To qualify for this, you have to be 14, pass a few tests, and then you can drive on the street with several restrictions, such as; You must have a licensed driver over 21 with you at all times.
2) Learners License. A 14 year old can get this after passing a few more tests, and then some of the restrictions will be eased. However, he'll still need a 21 year old licensed driver with him.
3)Intermediate License. You must be 16 to get this, by passing even more tests. With this license, you no longer have the requirement of needing an adult with you in the car.
Once you reach the age of 18, and can pass the requirements, you can get the Class D License, which HAS no restrictions.
I'm not sure of exactly how Texas does it, but I DO know that the EARLIEST you can get a learner's permit in that state is 15.