Final answer:
An E4 servicemember aboard ship undergoing non-judicial punishment cannot be awarded a bad-conduct discharge, which is a punishment reserved for court-martial proceedings.
Step-by-step explanation:
At a commanding officer's non-judicial punishment proceeding under Article 15 of the Uniform Code of Military Justice (UCMJ), an E4 servicemember aboard ship could be subject to various punishments. However, there are limitations on the punishments that can be awarded. An E4, or Petty Officer Third Class in the Navy and Coast Guard, cannot be awarded a bad-conduct discharge, as this punishment is only available through a court-martial. Other potential punitive measures that can be taken include restriction, reduction in rank, extra duties, forfeiture of pay, or a reprimand. It's important to note that the specifics can vary depending on the military branch and the discretion of the commanding officer.