Question

you may have ______ of the four watches .(add a correct determiner)

Answer 1

you may have one of the four watches.
I guess this must be the answer..
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Answer 2

Explanation:

You may have any of the four watches. The determiner like any is the correct answer for this particular sentence. You should keep in mind the sense of the sentence when you are putting a determiner in a sentence. It should reflect the correct meaning. Any watch can be chosen by you from the lot of four watches. This is main sense of the sentence.