-(으)ㄹ 수 있다
-(eu)l su itda
Not ability — an open door
The picture A door stands ahead of you. If it's open, you can walk through. What opened it might be your skill, a rule, or just today's schedule. -ㄹ 수 있다 is the door in front of you standing open; 못 is a wall someone else built in the same spot. Open way versus blocked way.
Where the picture shows up in -(으)ㄹ 수 있다
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your skill opens the door
저는 운전할 수 있어요.
jeo-neun un-jeon-hal su i-sseo-yo
I can drive.
Your own hand turns the key in the driver's seat, and the door in front of you swings open.
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asking whether the rule opens it
여기서 사진 찍을 수 있어요?
yeo-gi-seo sa-jin jji-geul su i-sseo-yo
Can I take photos here?
Looking up at the posted sign before raising the camera, letting the notice say whether the door is open.
The same form does duty for asking permission.
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today's circumstances open it
오늘은 일찍 갈 수 있어요.
o-neu-reun il-jjik gal su i-sseo-yo
I can leave early today.
Today's box on the calendar is empty, so the door out of work stands wide open.
Nothing to do with skill — the door is open only today.
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you open the door for someone
제가 도와드릴 수 있어요.
je-ga do-wa-deu-ril su i-sseo-yo
I can give you a hand.
You at the door, hand on the handle, pushing it open toward the other person.
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the door of possibility is ajar
비가 올 수도 있어요.
bi-ga ol su-do i-sseo-yo
It might rain.
The door not fully open — just a hand's width ajar.
With 수도 it leans away from ability and toward likelihood.
All of it in one picture
-ㄹ 수 있다 is one door standing in front of you. Your own hand on the key opens it and that reads as skill; a posted sign opens it and that reads as permission; an empty box on the calendar opens it and that reads as today's slack; your hand on the handle opens it for someone and that reads as help; a hand's width ajar and that reads as possibility. Across all five, what changes is who opened the door, never the door itself. So -ㄹ 수 있다 is never a boast about your ability — it is a report that the way is open right now.