"I cannot find my watch."
Translation:Ich kann meine Uhr nicht finden.
I have been told (in German class) that nicht is relatively flexible in this structure but it's position alters the meaning. For example "Ich kann nicht mein Uhr finden" negates "mein Uhr" and therefore implies that you cannot find your watch but did find something else.
I can see why the real meaning is better conveyed though "Ich kann mein Uhr nicht finden"
"Ich kann meine Schuhe nicht finden" seems to be the default answer for that exercise, so I would have to guess you made a typo in that one when you were writing your response. In both sentences, putting "nicht" after the noun is the best order.
(If you put "nicht" before the noun, you're specifically negating the noun so your sentence sounds like "I can't find my shoes, [but I can find e.g. my shirt]," and then it really needs that "sondern mein Hemd" at the end to make any sense.)
That's fair. Since this comment I read a couple articles about word order that really cleared it up for me so you're probably right about the typo. Here's the link to the 3rd of 3 articles covering word order in detail that really helped me for anyone interested https://yourdailygerman.com/german-word-order-3/
I feel like there isn't enough context to say what is being negated. Are you negating the find, the ability or the watch? We don't know.
I cannot find my watch. But I found other stuff. I cannot find my watch. But I can do other stuff. I cannot find my watch. But I want to find my watch.
Are the two places to put nicht grammatical as in:
lch kann meine Uhr nicht finden. lch kann nicht meine Uhr finden.
Or is one of them ungrammatical?
The nicht seems to be negaing Uhr in this sentence...
It's not; it's negating the verb. "Nicht" generally goes right before whatever it's negating, so if you wanted to say that what you can't find is specifically your watch, you would say "Ich kann nicht meine Uhr (sondern meinen Hut) finden."
Negating the verb is an exception; to do this you put the verb at the end (though before any infinitives and participles). In this exercise "nicht" is at the end (after everything but the infinitive), and so it's negating the verb-- the action of being able to find the watch.
Yes, it's accusative.
I thought it was dative If we have more than one verb (can and find)
That is not the case. You might be thinking of the fact that if a verb has more than one object, one object will typically be dative (but even this is not a hard-and-fast rule).
If you've got two verbs with one being an auxiliary verb like "können/müssen/sollen," then any noun objects are going to be the objects of the main verb and not the auxiliary. You can't "can something" or "should something," but you can "find something"; thus "meine Uhr" is the object of "finden." And it's the direct/accusative object because it's the thing you're (not) finding; you aren't, e.g., finding to it in a way that you would "give something to someone," which is what would typically indicate the dative.