The correct answer is B) draw a line through the entry, rewrite, and initial the correction. This is the proper way to correct a mistake in a logbook according to regulations governing the US Coast Guard Captain's License Examinations. The key is to never completely erase or obscure the original entry, as this could be considered tampering with an official record. Instead, the correction should be made by drawing a single line through the incorrect entry, rewriting the correct information, and initialing the change. This maintains the integrity of the logbook and provides a clear audit trail of any corrections made. The other options are incorrect because they either erase the original entry completely (A and D) or use excessive lines that could be considered an attempt to obscure the original record (C).