I'm writing in regarding the correct use of
... of yours.
For example, when should I say "I like your watch" or "I like this watch of yours"?
I looked on the internet and in my English grammar books but to no avail.
Thanks in advance for your help.
I would say that at least 95% of the time,
your watch will be the more expected and natural way to phrase it.
Sometimes you say things like
That new red car of yours looks like a blast to drive. but it would always be appropriate to say
Your new red car... instead.
belonging to you and thus both of the examples you quote is correct, although the latter
this watch of yours is more colloquial and would be regarded by some as poor English, even though it is widely used.
The word may also be used in letter as in
It should never be written
your's! Also look out for the difference between
you're - incorrect use of these words is a very common event in English.
Remember "your" means "belonging to you" whereas "you're" means "you are".