(A) A person while operating a motor vehicle under a conditional or a special restricted driver’s license who is convicted of a traffic offense or involved in an accident in which he was at fault shall have the removal of the restrictions postponed for twelve months and is not eligible to be issued a regular driver’s license until one year from the date of the last traffic offense or accident in which he was at fault or until he is seventeen years of age.

(B) A person while operating a motor vehicle under a beginner’s permit or a conditional or a special restricted driver’s license who is convicted of one or more point-assessable traffic offenses totaling six or more points, as determined by the values contained in § 56-1-720, shall have his license suspended by the Department of Motor Vehicles for six months. This suspension shall not preclude other penalties otherwise provided for the same violations.