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My teacher gives me two examples to state the difference between 不了 and 不动 as follows.

（A）我的腿受伤了，所以我走不了。

（B）我累得走不动。

I also read in Chinese Grammar Wiki but I still get confused.

(1) My teacher said that (B) cannot use 走不了, so can anyone point out situations that can use 不了 and 不动?

(2) In this sentence, should 不了 or 不动be used：这个书架我们两个抱不。。。

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This dictionary definition of 了 could help:

了 /liǎo/

动词

  1. 跟“得”或“不”组合用在动词后面，表示可能或不可能

干得了 / 去得了 / 这病好不了。

So, according to dictionaries, 不了 means something is impossible to achieve. E.g. 结束不了 (can't be over/finished)

不动 simply means to not move.

With all that above in mind, let's review your examples one by one:

我的腿受伤了，所以我走不了。// this is obvious that it denotes the sense of impossible to walk/leave.

我累得走不动 // the word 累(tired) suggests lack of energy, so 不动(can't move) make more sense.

这个书架我们两个抱不___ // in this case, if we put 动, it means you two can not make the bookshelf move. If we use 了, then it will implies that it's impossible for you two to hold the bookshelf and maybe you need more people to help. So, both are possible answers.

In fact, as you can see, 不了 and 不动 are quite different words. They just occasionally came across in some examples like yours.

Hope this could help.

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不 in 走不动 is a potential particle.

There are only two potential particles. one is 得(able to), the other is 不 (unable to)

走动 is a verb for 'walk around' or 'move around' and you can see it as [走 (verb)] + [动 (result complement)].

Insert a potential particle between the verb and the result complement indicate 'able' or 'unable' to achieve the result

  • 走(得)动 = (able to) walk and move around

  • 走(不)动 = (unable to) walk and move around

不了 in 走不了 act similarly as the auxiliary verb 'cannot' that modifies the verb 走. [走不了 = 不能走]

  • 走不了 can mean 'can't go' or 'can't walk'

  • 我的腿受伤了，所以我走不了 = My leg is hurt, so I can't go / can't walk

Your teacher said you can only say 我累得走不动, not 我累得走不了. He might be referring 走不了 as "can't go" . But 走 can also mean 'walk' , so 走不了 can also mean "can't walk"

(2) In this sentence, should 不了 or 不动 be used：这个书架我们两个抱不。。。

It should be 这个书架我们两个抱不动

抱 is the verb, 动 is the result complement:

  • 抱(得)动 = (able to) hold and move

  • 抱(不)动 = (unable to) hold and move

抱 is the verb 'hold' , 不了 is the auxiliary verb 'cannot'

  • 抱(不了) = cannot hold (may be it is too big)

More examples of difference between verb + 不了 (auxiliary verb) and [(verb) + (potential particles) + (result complement)]

  • 看見 -> 看不見 --> 人太多了，我看不見熊貓 - too many people, I can't see the panda (you try to see, but it is unsuccessful)

  • 看 -> 看不了 --> 今天要工作，看不了熊貓 - I have to work today, can't see the panda (you cannot see the panda for whatever reason, not for lacking the ability to see)

  • 去到 -> 去不到 --> 沒簽證去不到美國 - unable to go to America (you try to go, but it is unsuccessful)

  • 去 -> 去不了 --> 沒簽證去不了美國 - (you cannot go to America for whatever reason, not for lacking the ability to go)

不 in 看不見 (cannot successfully see) works on the result complement 見

不了 in 去不了 (cannot go) works on the verb 去

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V + 不了

This potential complement usually describes something that you generally can't because of an external factor out of your control. 没有办法！

我的腿受伤了，所以我走不了 "I can't walk because my leg is injured"

I didn't decide to get injured (did I?)

这数学问题太难，我帮不了你 "This math problem is too difficult, I can't help you"

I'm unable to help you because I lack the necessary skills.

这是非法的，我做不了 "This is illegal, I can't do that"

I can't do that because the law forbids me to do that

V + 不动

This instead describes your own physical inability, and not an external hinderance.

When talking about physical feats though, you might think: "Wait, if I'm physically unable to do something, it's not really under my control, is it?". Well technically it is:

我累得走不动 "I'm so tired I can't walk"

In this example I can't walk because I'm too tired, but I could theoretically force myself to keep going (and collapse shortly after).

Therefore here:

这个书架，我们俩抱不动

The two of us can't physically carry the shelf, but there's no external factor stopping us from doing it anyway (and get crushed afterwards...).

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  • "这是非法的，我做不了 ", 这是非法的，我不能做 makes more sense. (you also translated as "can't'")
    – dan
    Jun 29, 2020 at 14:06
  • @dan in that example, would you say that 我做不了 is wrong, less good than 能 or equivalent? In multiple occasions I've heard natives using 不了 when talking about the impossibility to do something because of rules preventing them. I wonder if those were euphemisms or something... 推卸责任...
    – blackgreen
    Jun 29, 2020 at 14:32
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    It's not a language issue but a logic one. 我做不了 means you can't achieve something. 这是非法的 (something illegal) is not the reason that you can't achieve it, but can't/shouldn't do it. E. g. you won't kill someone because that's illegal. However, you still have ability to kill someone. But colloquially, no one would care about this nuance. People might use as they wish. If it didn't get across, then they just clarify.
    – dan
    Jun 29, 2020 at 14:49
  • In practice, it's possible that some regulations block you to achieve something. In that case, 我做不了 makes much sense. E. g. 没有政府批文，这事我做不了。
    – dan
    Jun 29, 2020 at 14:57

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