NBC’s “Apprentice” finale earned Thursday’s highest ratings. Nielsen estimated that 12.1 million viewers tuned in from 9 to 11 p.m., the largest audience since the finale of “The Apprentice 4” in December 2005. Ratings for the series had fallen since its inaugural 2004 season, which averaged almost 21 million viewers an episode, reaching its lowest level a year ago, with an average of just over seven million viewers. For the night over all, NBC ranked first, just ahead of CBS, which broadcast N.C.A.A. basketball. Fox was third and ABC fourth.