Final answer:
An E-6's board eligibility for promotion within the United States Navy or Coast Guard is determined by a fitness report or performance evaluation, in addition to their examination scores.
Step-by-step explanation:
Beyond the normal examination score, a fitness report or performance evaluation determines an E-6's board eligibility. These evaluations are a comprehensive record of a sailor's performance and conduct during their service, encompassing various aspects of their duties, leadership abilities, and professional development. The E-6 is the pay grade for a Petty Officer First Class in the United States Navy and Coast Guard, and achieving this rank includes a combination of examination scores, time in service, and these evaluative reports.