동지(Donji) = the winter solstice?? <em>yes! 冬至 in Chinese is similar sound dongzhi)</em>

I ate red been soup(팥죽, patjuk) today.
Because today is 동지(the winter solstice) of the lunar calendar. <em>(not just lunar calendar, it is the northern world's winter solstice)</em> 
I don't exactly know how to say the 동지 in English. <em>(you are correct, shortest day)</em>.
So I searched the internet dictionary and I found the word 'the winter solstice'.
But I'm not sure that word.
Anyway, I ate at around 11 pm
Perhaps I will not sleep for a while.ㅠㅠ

<em>No corrections required for the English.  Northern Winter Solstice is ipso facto Southern Summer Solstice</em>

동지(Donji) = the winter solstice??

I ate red been bean soup(팥죽, patjuk) today, Beacause because today is 동지(the winter solstice??) of the lunar calendar.
I don't exactly know how to say the 동지 in English.
So I searched the internet dictionary and I found the word term 'the winter solstice'.
But I'm not sure about that word.
Anyway, I ate at around 11 p.m. 
Perhaps I will not sleep for a while.ㅠㅠ

corrections

suggestions

The term you found "winter solstice" is correct. 

I deleted "at" because the preposition "around" is enough.  I think many people might use them together, but I think it is grammatically incorrect.

How was the 팥죽?  :)