까지
kka-ji
까지 is a wall — and the wall is inside
The picture You are drawing a line and you set a wall down: stop here. Everything up to and including the wall counts.
Where the picture shows up in 까지
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a wall in time
여섯 시까지 끝낼게요.
yeo-seot si-kka-ji kkeun-nael-ge-yo
I'll finish by six.
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the end of the road
서울역까지 가 주세요.
seo-ul-lyeok-kka-ji ga ju-se-yo
To Seoul Station, please.
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the wall called a deadline
서류는 내일까지 주세요.
seo-ryu-neun nae-il-kka-ji ju-se-yo
Give me the papers by tomorrow.
내일까지 includes tomorrow itself. It is not 'before tomorrow'.
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the end of the range
이 페이지까지 읽고 오세요.
i pe-i-ji-kka-ji il-go o-se-yo
Read up to this page before you come.
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a wall it should not have crossed
늦었는데 비까지 오네요.
neu-jeon-neun-de bi-kka-ji o-ne-yo
Late, and now it's raining on top of that.
도 just adds one more; 까지 adds 'I never expected it to come this far'.