会/能/可以
huì / néng / kěyǐ
Three locks on the same door marked can
The picture One door labelled I can, with three locks on it. 会 opens with what you have learned, 能 with what your body and your day allow, 可以 only when someone else turns the key. In refusals, 不可以 is a rule pushing back — you may not — while 不能 is circumstance pushing back: I'm not in a position to.
Where the picture shows up in 会/能/可以
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the lock learning opens
我会开车，可是今天喝酒了。
wǒ huì kāichē, kěshì jīntiān hē jiǔ le
I do know how to drive, but I've been drinking today.
Someone who knows the wheel perfectly well, car key in hand, looking down at a glass of beer
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the lock circumstances jam
今天我不能加班，得去接孩子。
jīntiān wǒ bù néng jiābān, děi qù jiē háizi
I can't stay late today — I have to pick up my kid.
Standing at your desk at clocking-off time, bag in hand, eyes going from the clock to the nursery door
Use 不能 when the situation blocks you, not your skill.
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the key someone else holds
请问这儿可以抽烟吗？
qǐngwèn zhèr kěyǐ chōuyān ma
Excuse me, is smoking allowed here?
Cigarette halfway to your lips, turning to catch the shop owner's eye first
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how much your body can put out
他一天能走两万步。
tā yì tiān néng zǒu liǎng wàn bù
He can walk twenty thousand steps a day.
A step counter at the end of the day reading 20,000
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the way things already go
天气预报说明天会下雨。
tiānqì yùbào shuō míngtiān huì xià yǔ
The forecast says it'll rain tomorrow.
Raindrop icons dropping onto tomorrow's square on the weather map on TV
会 is what has been learned into something, so it also covers what the world reliably does — that is, will.
All of it in one picture
Knowing how to drive is 会, something learning left in the body; not being able to stay late is 能, blocked by the shape of today; asking whether you may smoke is 可以, the key in somebody else's hand. Twenty thousand steps is the size of the output a body can manage, so 能 again, and rain forecast for tomorrow is 会 — the way the world already tends to go. Three words at the same door, each asking something different: have you learned it, are you up to it now, are you allowed?