An alternative way to solve this word-ordering question is to start from the fixed ending constraint and build the sentence backward, rather than starting from the subject and moving forward.
The words are: 1-AT, 2-EVENING, 3-AGAIN, 4-LAST, 5-MET, 6-WE, 7-HER, 8-HOSPITAL, 9-THE. The condition requires an affirmative sentence in which the part of the day, "evening" (word 2), is the very last word.
Working backward: the last two words must form the time phrase "last evening," giving the ending 4 (LAST), 2 (EVENING). Just before the time phrase comes the place phrase, which must read "at the hospital," giving 1 (AT), 9 (THE), 8 (HOSPITAL). Before the place phrase, the core statement needs a subject, verb, object, and an adverb of repetition to form "we met her again," giving 6 (WE), 5 (MET), 7 (HER), 3 (AGAIN).
Joining these backward-built blocks in forward order gives: We met her again at the hospital last evening, which is a complete, affirmative sentence ending in the part of the day as required.
Converting this to the index sequence gives 6, 5, 7, 3, 1, 9, 8, 4, 2.
Hence, the correct answer is \[ \boxed{\text{657319842}} \].