What does すべき mean in 'この記念すべき日'?

Question

I have the following sentence from a subtitle

本日は この記念すべき日を迎える事が できた事に 感極まる思いであります｡

I also have the translated subtitle.

Today we are able to celebrate this memorable day, a day filled with emotions.

First of all, is that translation accurate and complete? Because I'm having trouble understanding what 「記念すべき日」 means. My best guess is 'day we should celebrate'. But if that's it, I can't really figure out how to fit it into the rest of the sentence. And 「迎える」 having about 15 meanings in the dictionary is making things even more difficult.

Answer 1

すべき is する＋べき. べき basically means should.

記念すべき日 is then 記念する + べき + 日 and means as you surmised, a day that should be celebrated or a day we should celebrate.

The main action is 感極まる思いであります, which is basically a fancy way of saying extremely emotional. Why does the speaker feel so emotional? The に tells you that この記念すべき日を迎える事ができた事 is what the speaker feels so emotional towards.

I think the important thing about the rest of the sentence is that all the 事s act as nominalizers. 迎える means something like to arrive at this day (It's definition 4 on デジタル大辞泉).

この記念すべき日 = This day that should be celebrated

[この記念すべき日]を迎える = Arrive at this day that should be celebrated

[この記念すべき日を迎える事]ができた = We are able to arrive at this day that should be celebrated (事 makes the previous phrase a noun phrase)

[この記念すべき日を迎える事ができた]事 = The fact that we are able to arrive at this day that should be celebrated (事 makes the previous phrase a noun phrase)

So then the speaker is saying that:

today I am extremely emotional at being able to arrive at this day that should be celebrated.

Honestly that just sounds pretty bad in English.